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Vahab S. Mirrokni

Vahab S. Mirrokni

Vahab Mirrokni is a Google Fellow and VP at Google Research, leading algorithm and optimization research groups at Google. These research teams include: market algorithms, large-scale graph mining, and large-scale optimization. Previously he was a distinguished scientist and senior research director at Google. He received his PhD from MIT in 2005 and his B.Sc. from Sharif University of Technology in 2001. He joined Google Research in 2008, after research positions at Microsoft Research, MIT and Amazon.com. He is the co-winner of best paper awards at KDD, ACM EC, and SODA. His research areas include algorithms, distributed and stochastic optimization, and computational economics. Recently he has been working on various algorithmic problems in machine learning, online optimization and mechanism design, and large-scale graph-based learning . His full publication list by year can be found here . He also has an out-dated personal homepage.
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    Sequential Attention for Feature Selection
    Taisuke Yasuda
    Proceedings of the 11th International Conference on Learning Representations (2023)
    Preview abstract Feature selection is the problem of selecting a subset of features for a machine learning model that maximizes model quality subject to a budget constraint. For neural networks, prior methods, including those based on L1 regularization, attention, and other techniques, typically select the entire feature subset in one evaluation round, ignoring the residual value of features during selection, i.e., the marginal contribution of a feature given that other features have already been selected. We propose a feature selection algorithm called Sequential Attention that achieves state-of-the-art empirical results for neural networks. This algorithm is based on an efficient one-pass implementation of greedy forward selection and uses attention weights at each step as a proxy for feature importance. We give theoretical insights into our algorithm for linear regression by showing that an adaptation to this setting is equivalent to the classical Orthogonal Matching Pursuit (OMP) algorithm, and thus inherits all of its provable guarantees. Our theoretical and empirical analyses offer new explanations towards the effectiveness of attention and its connections to overparameterization, which may be of independent interest. View details
    Approximately Optimal Core Shapes for Tensor Decompositions
    Mehrdad Ghadiri
    Proceedings of the 40th International Conference on Machine Learning (2023), pp. 11237-11254
    Preview abstract This work studies the combinatorial optimization problem of finding an optimal core tensor shape, also called multilinear rank, for a size-constrained Tucker decomposition. We give an algorithm with provable approximation guarantees for its reconstruction error via connections to higher-order singular values. Specifically, we introduce a novel Tucker packing problem, which we prove is NP-hard, and give a polynomial-time approximation scheme based on a reduction to the 2-dimensional knapsack problem with a matroid constraint. We also generalize our techniques to tree tensor network decompositions. We implement our algorithm using an integer programming solver, and show that its solution quality is competitive with (and sometimes better than) the greedy algorithm that uses the true Tucker decomposition loss at each step, while also running up to 1000x faster. View details
    Learning Rate Schedules in the Presence of Distribution Shift
    Adel Javanmard
    Pratik Worah
    Proceedings of the 40th International Conference on Machine Learning (2023), pp. 9523-9546
    Preview abstract We design learning rate schedules that minimize regret for SGD-based online learning in the presence of a changing data distribution. We fully characterize the optimal learning rate schedule for online linear regression via a novel analysis with stochastic differential equations. For general convex loss functions, we propose new learning rate schedules that are robust to distribution shift, and we give upper and lower bounds for the regret that only differ by constants. For non-convex loss functions, we define a notion of regret based on the gradient norm of the estimated models and propose a learning schedule that minimizes an upper bound on the total expected regret. Intuitively, one expects changing loss landscapes to require more exploration, and we confirm that optimal learning rate schedules typically increase in the presence of distribution shift. Finally, we provide experiments for high-dimensional regression models and neural networks to illustrate these learning rate schedules and their cumulative regret. View details
    Preview abstract The streaming model of computation is a popular approach for working with large-scale data. In this setting, there is a stream of items and the goal is to compute the desired quantities (usually data statistics) while making a single pass through the stream and using as little space as possible. Motivated by the importance of data privacy, we develop differentially private streaming algorithms under the continual release setting, where the union of outputs of the algorithm at every timestamp must be differentially private. Specifically, we study the fundamental $\ell_p$ $(p\in [0,+\infty))$ frequency moment estimation problem under this setting, and give an $\varepsilon$-DP algorithm that achieves $(1+\eta)$-relative approximation $(\forall \eta\in(0,1))$ with $\mathrm{poly}\log(Tn)$ additive error and uses $\mathrm{poly}\log(Tn)\cdot \max(1, n^{1-2/p})$ space, where $T$ is the length of the stream and $n$ is the size of the universe of elements. Our space is near optimal up to poly-logarithmic factors even in the non-private setting. To obtain our results, we first reduce several primitives under the differentially private continual release model, such as counting distinct elements, heavy hitters and counting low frequency elements, to the simpler, counting/summing problems in the same setting. Based on these primitives, we develop a differentially private continual release level set estimation approach to address the $\ell_p$ frequency moment estimation problem. We also provide a simple extension of our results to the harder sliding window model, where the statistics must be maintained over the past $W$ data items. View details
    Preview abstract Although costs are prevalent in ad auctions, not many auction theory works study auction design in the presence of cost in the classic settings. One reason is that most auctions design in the setting without cost directly generalize to the setting with cost when the bidders maximizing quasi-linear utility. However, as auto-bidding becomes a major choice of advertisers in online advertising, the distinction from the underlying behavior model often leads to different solutions of many well-studied auctions. In the context of ad auctions with cost, VCG achieves optimal welfare with quasi-linear utility maximizing bidders, while has 0 welfare approximation guarantee with value maximizing bidders who follow the optimization behind common auto-bidding algorithms. In this paper, we prove that the approximation welfare guarantee of VCG auction can be significantly improved by a minimal change --- introducing cost multipliers. We note that one can use either one multiplier per auction or one multiplier per bidder, but one global multiplier across all auctions and bidders does not work. Finally, to echo with our theoretical results, we conduct empirical evaluations using semi-synthetic data derived from real auction data of a major advertising platform. View details
    Preview abstract We study the private $k$-median and $k$-means clustering problem in $d$ dimensional Euclidean space. By leveraging tree embeddings, we give an efficient and easy to implement algorithm, that is empirically competitive with state of the art non private methods. We prove that our method computes a solution with cost at most $O(d^{3/2}\log n)\cdot OPT + O(k d^2 \log^2 n / \epsilon^2)$, where $\epsilon$ is the privacy guarantee. (The dimension term, $d$, can be replaced with $O(\log k)$ using standard dimension reduction techniques.) Although the worst-case guarantee is worse than that of state of the art private clustering methods, the algorithm we propose is practical, runs in near-linear, $\tilde{O}(nkd)$, time and scales to tens of millions of points. We also show that our method is amenable to parallelization in large-scale distributed computing environments. In particular we show that our private algorithms can be implemented in logarithmic number of MPC rounds in the sublinear memory regime. Finally, we complement our theoretical analysis with an empirical evaluation demonstrating the algorithm's efficiency and accuracy in comparison to other privacy clustering baselines. View details
    Preview abstract We study the differentially private (DP) $k$-means and $k$-median clustering problems of $n$ points in $d$-dimensional Euclidean space in the massively parallel computation (MPC) model. We provide two near-optimal algorithms where the near-optimality is in three aspects: they both achieve (1). $O(1)$ parallel computation rounds, (2). near-linear in $n$ and polynomial in $k$ total computational work (i.e., near-linear running time in the sequential setting), (3). $O(1)$ relative approximation and $\text{poly}(k, d)$ additive error, where $\Omega(1)$ relative approximation is provably necessary even for any polynomial-time non-private algorithm, and $\Omega(k)$ additive error is a provable lower bound for any polynomial-time DP $k$-means/median algorithm. Our two algorithms provide a tradeoff between the relative approximation and the additive error: the first has $O(1)$ relative approximation and $\sim (k^{2.5} + k^{1.01} \sqrt{d})$ additive error, and the second one achieves $(1+\gamma)$ relative approximation to the optimal non-private algorithm for an arbitrary small constant $\gamma>0$ and with $\text{poly}(k, d)$ additive error for a larger polynomial dependence on $k$ and $d$. To achieve our result, we develop a general framework which partitions the data and reduces the DP clustering problem for the entire dataset to the DP clustering problem for each part. To control the blow-up of the additive error introduced by each part, we develop a novel charging argument which might be of independent interest. View details
    Preview abstract The conclusions of randomized controlled trials may be biased when the outcome of one unit depends on the treatment status of other units, a problem known as interference. In this work, we study interference in the setting of one-sided bipartite experiments in which the experimental units---where treatments are randomized and outcomes are measured---do not interact directly. Instead, their interactions are mediated through their connections to interference units on the other side of the graph. Examples of this type of interference are common in marketplaces and two-sided platforms. The cluster-randomized design is a popular method to mitigate interference when the graph is known, but it has not been well-studied in the one-sided bipartite experiment setting. In this work, we formalize a natural model for interference in one-sided bipartite experiments using the exposure mapping framework. We first exhibit settings under which existing cluster-randomized designs fail to properly mitigate interference under this model. We then show that minimizing the bias of the difference-in-means estimator under our model results in a balanced partitioning clustering objective with a natural interpretation. We further prove that our design is minimax optimal over the class of linear potential outcomes models with bounded interference. We conclude by providing theoretical and experimental evidence of the robustness of our design to a variety of interference graphs and potential outcomes models. View details
    Preview abstract A fundamental procedure in the analysis of massive datasets is the construction of similarity graphs. Such graphs play a key role for many downstream tasks, including clustering, classification, graph learning, and nearest neighbor search. For these tasks, it is critical to build graphs which are sparse yet still representative of the underlying data. The benefits of sparsity are twofold: firstly, constructing dense graphs is infeasible in practice for large datasets, and secondly, the runtime of downstream tasks is directly controlled by the sparsity of the similarity graph. In this work, we present Stars: a highly scalable method for building extremely sparse graphs via two-hop spanners, which are graphs where similar points are connected by a path of length at most two. Stars can construct two-hop spanners with significantly fewer similarity comparisons, which are a major bottleneck for learning based models where comparisons are expensive to evaluate. Theoretically, we demonstrate that Stars builds a graph in nearly-linear time, where approximate nearest neighbors are contained within two-hop neighborhoods. To complement our results, we have deployed Stars for multiple data sets allowing for graph building at the Tera-Scale, i.e., for graphs with hundreds of billions of nodes and tens of trillions of edges. We evaluate the performance of Stars for clustering and graph learning, and demonstrate 10~1000-fold improvements in pairwise similarity comparisons and significant improvements in runtime with negligible quality loss. View details
    Preview abstract The conclusions of randomized controlled trials may be biased when the outcome of one unit depends on the treatment status of other units, a problem known as interference. In this work, we study interference in the setting of one-sided bipartite experiments in which the experimental units---where treatments are randomized and outcomes are measured---do not interact directly. Instead, their interactions are mediated through their connections to interference units on the other side of the graph. Examples of this type of interference are common in marketplaces and two-sided platforms. The cluster-randomized design is a popular method to mitigate interference when the graph is known, but it has not been well-studied in the one-sided bipartite experiment setting. In this work, we formalize a natural model for interference in one-sided bipartite experiments using the exposure mapping framework. We first exhibit settings under which existing cluster-randomized designs fail to properly mitigate interference under this model. We then show that minimizing the bias of the difference-in-means estimator under our model results in a balanced partitioning clustering objective with a natural interpretation. We further prove that our design is minimax optimal over the class of linear potential outcomes models with bounded interference. We conclude by providing theoretical and experimental evidence of the robustness of our design to a variety of interference graphs and potential outcomes models. View details
    Preview abstract We consider $k$-means clustering of $n$ data points in Euclidean space in the Massively Parallel Computation (MPC) model, a computational model which is an abstraction of modern massively parallel computing system such as MapReduce. There was a conditional lower bound showing that getting $O(1)$-approximate $k$-means solution for general input points using $o(\log n)$ rounds in the MPC model is impossible. However, the real-world data points usually have better structures. One instance of interest is the set of data points which is perturbation resilient [Bilu \& Linial'2010]. In particular, a point set is $\alpha$-perturbation resilient for $k$-means if perturbing pairwise distances by multiplicative factors in the range $[1,\alpha]$ does not change the optimum $k$-means clusters. We bypass the worst case lower bound by considering the perturbation resilient input points and showing $o(\log n)$ rounds $k$-means clustering algorithms for these instances in the MPC model. Specifically, we show a fully scalable $(1+\varepsilon)$-approximate $k$-means clustering algorithm for $O(\alpha)$-perturbation resilient instance in the MPC model using $O(\log\log n)$ rounds and $\widetilde{O}_{\varepsilon,d}(n^{1+1/\alpha^2})$ total space. If the space per machine is sufficient larger than $k$, i.e., at least $k\cdot n^{\Omega(1)}$, we also develop an optimal $k$-means clustering algorithm for $O(\alpha)$-perturbation resilient instance in the MPC model using $O(\log\log n)$ rounds and $\widetilde{O}_d(n\cdot(n^{1/\alpha^2}+k))$ total space. View details
    Preview abstract Personalized PageRank (PPR) is a fundamental tool in unsupervised learning of graph representations such as node ranking, labeling, and graph embedding. However, while data privacy is one of the most important recent concerns, existing PPR algorithms are not designed to protect user privacy. PPR is highly sensitive to the input graph edges: the difference of only one edge may cause a big change in the PPR vector, potentially leaking private user data. In this work, we propose an algorithm which outputs an approximate PPR and has provably bounded sensitivity to input edges. In addition, we prove that our algorithm achieves similar accuracy to non-private algorithms when the input graph has large degrees. Our sensitivity-bounded PPR directly implies private algorithms for several tools of graph learning, such as, differentially private (DP) PPR ranking, DP node classification, and DP node embedding. To complement our theoretical analysis, we also empirically verify the practical performances of our algorithms. View details
    Preview abstract Obtaining scalable algorithms for hierarchical agglomerative clustering (HAC) is of significant interest due to the massive size of real-world datasets. At the same time, efficiently parallelizing HAC is difficult due to the seemingly sequential nature of the algorithm. In this paper, we address this issue and present ParHAC, the first efficient parallel HAC algorithm with sublinear depth for the widely-used average-linkage function. In particular, we provide a (1+ϵ)-approximation algorithm for this problem on m edge graphs using O(m polylog m) work and poly-logarithmic depth. Moreover, we show that obtaining similar bounds for exact average-linkage HAC is not possible under standard complexity-theoretic assumptions. We complement our theoretical results with a comprehensive study of the ParHAC algorithm in terms of its scalability, performance, and quality, and compare with several state-of-the-art sequential and parallel baselines. On a broad set of large publicly-available real-world datasets, we find that ParHAC obtains a 50.1x speedup on average over the best sequential baseline, while achieving quality similar to the exact HAC algorithm. We also show that ParHAC can cluster one of the largest publicly available graph datasets with 124 billion edges in a little over three hours using a commodity multicore machine. View details
    Preview abstract Motivated by data analysis and machine learning applications, we consider the popular high-dimensional Euclidean $k$-median and $k$-means problems. We propose a new primal-dual algorithm, inspired by the classic algorithm of Jain and Vazirani and the recent algorithm of Ahmadian et al.. Our algorithm achieves an approximation ratio of respectively 2.40... and 5.95... for Euclidean $k$-median and $k$-means improving upon the 2.60... of Ahmadian et al. and the 6.12.. of Grandoni et al.. View details
    Preview abstract We study the design of revenue-maximizing mechanisms for value-maximizing agents with budget constraints. Agents have return-on-spend constraints requiring a minimum amount of value per unit of payment made and budget constraints limiting their total payments. The agents' only private information are the minimum admissible ratios on the return-on-spend constraint, referred to as the target ratios. Our work is motivated by internet advertising platforms, where automated bidders are increasingly being adopted by advertisers to purchase advertising opportunities on their behalf. Instead of specifying bids for each keyword, advertiser set high-level goals, such as maximizing clicks, and targets on cost-per-clicks or return-on-spend, and the platform automatically purchases opportunities by bidding in different auctions. We present a model that abstracts away the complexities of the auto-bidding procurement process that is general enough to accommodate many allocation mechanisms such as auctions, matchings, etc. We reduce the mechanism design problem when agents have private target ratios to a challenging non-linear optimization problem with monotonicity constraints. We provide a novel decomposition approach to tackle this problem that yields insights into the structure of optimal mechanisms and show that surprising features stem from the interaction on budget and return-on-spend constraints. Our optimal mechanism, which we dub the target-clipping mechanism, has an appealing structure: it sets a threshold on the target ratio of each agent, targets above the threshold are allocated efficiently, and targets below are clipped to the threshold. View details
    Design and analysis of bipartite experiments under a linear exposure-response model
    Christopher Harshaw
    Fredrik Savje
    David Eisenstat
    Proceedings of the 23rd ACM Conference on Economics and Computation (2022), pp. 606
    Preview abstract A bipartite experiment consists of one set of units being assigned treatments and another set of units for whichwe measure outcomes. The two sets of units are connected by a bipartite graph, governing how the treatedunits can affect the outcome units. In this paper, we consider estimation of the average total treatment effectin the bipartite experimental framework under a linear exposure-response model. We introduce the ExposureReweighted Linear (ERL) estimator, and show that the estimator is unbiased, consistent and asymptoticallynormal, provided that the bipartite graph is sufficiently sparse. To facilitate inference, we introduce an unbiasedand consistent estimator of the variance of theERLpoint estimator. In addition, we introduce a cluster-baseddesign,Exposure-Design, that uses heuristics to increase the precision of theERLestimator by realizinga desirable exposure distribution. Finally, we demonstrate the application of the described methodology tomarketplace experiments using a publicly available Amazon user-item review dataset. View details
    Synthetic Design: An Optimization Approach to Experimental Design with Synthetic Controls
    Guido Imbens
    Jann Spiess
    Khashayar Khosravi
    Miles Lubin
    35th Conference on Neural Information Processing Systems (NeurIPS 2021) (2021)
    Preview abstract We investigate the optimal design of experimental studies that have pre-treatment outcome data available. The average treatment effect is estimated as the difference between the weighted average outcomes of the treated and control units. A number of commonly used approaches fit this formulation, including the difference-in-means estimator and a variety of synthetic-control techniques. We propose several methods for choosing the set of treated units in conjunction with the weights. Observing the NP-hardness of the problem, we introduce a mixed-integer programming formulation which selects both the treatment and control sets and unit weightings. We prove that these proposed approaches lead to qualitatively different experimental units being selected for treatment. We use simulations based on publicly available data from the US Bureau of Labor Statistics that show improvements in terms of mean squared error and statistical power when compared to simple and commonly used alternatives such as randomized trials. View details
    Preview abstract Graph clustering and community detection are central problems in modern data mining. The increasing need for analyzing billion-scale data calls for faster and more scalable algorithms for these problems. There are certain trade-offs between the quality and speed of such clustering algorithms. In this paper, we design scalable algorithms that achieve high quality when evaluated based on ground truth. We develop a generalized sequential and shared-memory parallel framework based on the LambdaCC objective (introduced by Veldt et al.), which encompasses modularity and correlation clustering. Our framework consists of highly-optimized implementations that scale to large data sets of billions of edges and that obtain high-quality clusters compared to ground-truth data, on both unweighted and weighted graphs. Our empirical evaluation shows that this framework improves the state-of-the-art trade-offs between speed and quality of scalable community detection. For example, on a 30-core machine with two-way hyper-threading, our implementations achieve orders of magnitude speedups over other correlation clustering baselines, and up to 28.44x speedups over our own sequential baselines while maintaining or improving quality View details
    Preview abstract In classic auction theory, reserve prices are known to be effective for improving revenue for the auctioneer against quasi-linear utility maximizing bidders. The introduction of reserve prices, however, usually do not help improve total welfare of the auctioneer and the bidders. In this paper, we focus on value maximizing bidders with return on spend constraints---a paradigm that has drawn considerable attention recently as more advertisers adopt auto-bidding algorithms in advertising platforms---and show that the introduction of reserve prices has a novel impact on the market. Namely, by choosing reserve prices appropriately the auctioneer can improve not only the total revenue but also the total welfare. Our results also demonstrate that reserve prices are robust to bidder types, i.e., reserve prices work well for different bidder types, such as value maximizers and utility maximizers, without using bidder type information. We generalize these results for a variety of auction mechanisms such as VCG, GSP, and first-price auctions. Moreover, we show how to combine these results with additive boosts to improve the welfare of the outcomes of the auction further. Finally, we complement our theoretical observations with an empirical study confirming the effectiveness of these ideas using data from online advertising auctions. View details
    Preview abstract Internet advertisers are increasingly adopting automated bidders to buy advertising opportunities. Automated bidders simplify the procurement process by allowing advertisers to specify their goals and then bidding on their behalf in the auctions that are used to sell advertising slots. One popular goal adopted by advertisers is to maximize their clicks (or conversions) subject to a return on spend (RoS) constraint, which imposes that the ratio of total value to total spend is greater than a target ratio specified by the advertisers. The emergence of automated bidders brings into question whether the standard mechanisms used to sold ads are still effective in this new landscape. Thus motivated, in this paper we study the problem of characterizing optimal mechanisms for selling an item to one of multiple agents with return on spend constraints when either the values or target ratios are private. We consider two objectives for the agents: value maximization, which is becoming the prevalent objective in advertising markets, and utility maximization, which is the de facto paradigm in economic theory. Our goal is to understand the impact of the agents' private information and their objectives on the seller's revenue, and determine whether the first-best revenue, which is the optimal revenue without private information, is achievable. View details
    Non-Clairvoyant Dynamic Mechanism Design with Budget Constraints and Beyond
    Proceedings of the 22nd ACM Conference on Economics and Computation (2021), pp. 369
    Preview abstract We provide a general design framework for dynamic mechanisms under complex environments, coined Lossless History Compression mechanisms. Lossless history compression mechanisms compress the history into a state carrying the least historical information without losing any generality in terms of either revenue or welfare. In particular, the characterization works for almost arbitrary constraints on the outcomes, and any objective function defined on the historical reports, allocations, and the cumulative payments. We then apply our framework to design a non-clairvoyant dynamic mechanism under budget and ex-post individual rationality constraints that is dynamic incentive-compatible and achieves non-trivial revenue performance, even without any knowledge about the future. In particular, our dynamic mechanism obtains a constant approximation to the optimal dynamic mechanism having access to all information in advance. To the best of our knowledge, this is the first dynamic mechanism that achieves a constant approximation and strictly respects dynamic incentive-compatibility and budget constraints without relying on any forecasts of the future. View details
    Preview abstract Online advertisements are primarily sold via repeated auctions with reserve prices. In this paper, we study how to set reserves to boost revenue based on the historical bids of strategic buyers, while controlling the impact of such a policy on the incentive compatibility of the repeated auctions. Adopting an incentive compatibility metric which quantifies the incentives to shade bids, we propose a novel class of reserve pricing policies and provide analytical tradeoffs between their revenue performance and bid-shading incentives. The policies are inspired by the exponential mechanism from the literature on differential privacy, but our study uncovers mechanisms with significantly better revenue-incentive tradeoffs than the exponential mechanism in practice. We further empirically evaluate the tradeoffs on synthetic data as well as ad auction data from a major ad exchange to verify and support our theoretical findings. View details
    Preview abstract Metric clustering is a fundamental primitive in machine learning with several applications for mining massive data-sets. An important example of metric clustering is the $k$-center problem. While this problem has been extensively studied in distributed settings, all previous algorithms require $\Omega(k)$ space per machine and $\Omega(n k)$ total work. In this paper, we develop the first highly scalable approximation algorithm for $k$-center clustering requiring $o(k)$ space per machine with $o(n k)$ total work. In particular, our algorithm needs $\widetilde{O}(n^{\eps})$ space per machine and $\tilde{O}(n^{1+\epsilon})$ total work, and computes an $O(\log \log \log n)$-approximation of the problem by selecting $(1+o(1))k$ centers in $O(\log \log n)$ rounds. This is achieved by introducing core-sets of truly sublinear size. View details
    Preview abstract Auto-bidding has become one of the main options for bidding in online advertisements, in which advertisers only need to specify high-level objectives and leave the complex task of bidding to auto-bidders. In this paper, we propose a family of auctions with boosts to improve welfare for auto-bidders with both return on ad spend constraints and budget constraints. Our empirical results validate our theoretical findings and show that both the welfare and revenue can be improved by selecting the weight of the boosts properly. View details
    Non-Excludable Dynamic Mechanism Design
    Proceedings of the 2021 ACM-SIAM Symposium on Discrete Algorithms (SODA), SIAM, pp. 1357-1373
    Preview abstract Dynamic mechanism design expands the scope on what type of allocation rules can be implemented and what revenue can be extracted when compared to static mechanisms. The case of excludable environments (i.e. one player can be de-allocated while keeping the allocation of the remaining players intact) is very well understood. The mechanisms in the literature don’t extend to the non-excludable environments. Two prototypical examples of such environments are: (i) public projects, where all players must have the same allocation; and (ii) non-disposable goods, where each item must be allocated to some player. We show a general mechanism that can asymptotically extract the full surplus in such environments. Moreover, we fully characterize which abstract mechanism design environments allow for full surplus extraction in the limit. Our characterization is based on the geometry of achievable utility sets – a convex set characterizing the expected utility profiles that can be implemented in a static mechanism. View details
    Preview abstract We study the widely used hierarchical agglomerative clustering (HAC) algorithm on edge-weighted graphs. We define an algorithmic framework for hierarchical agglomerative graph clustering that provides the first efficient Õ(m) time exact algorithms for classic linkage measures, such as complete- and WPGMA-linkage, as well as other measures. Furthermore, for average-linkage, arguably the most popular variant of HAC, we provide an algorithm that runs in Õ (n sqrt(m)) time. For this variant, this is the first exact algorithm that runs in subquadratic time, as long as m=n^(2−ϵ) for some constant ϵ>0. We complement this result with a simple ϵ-close approximation algorithm for average-linkage in our framework that runs in Õ (m) time. As an application of our algorithms, we consider clustering points in a metric space by first using k-NN to generate a graph from the point set, and then running our algorithms on the resulting weighted graph. We validate the performance of our algorithms on publicly available datasets, and show that our approach can speed up clustering of point datasets by a factor of 20.7--76.5x. View details
    Preview abstract We study an intermediary model between stochastic and adversarial bandits, which we term adversarial scaling, where the rewards are a product between a stochastic component and an adversarial component shared by all arms. This can be viewed as a model where the ratios between the mean rewards remain fixed, but the magniture of rewards is rescaled by an adaptive adversary. We obtain logarithmic regret bounds for this setting. As a by-product we improve the regret of purely stochastic bandits in the special case where all the means are small. Finally we show that classical algorithms such as UCB and Thompson Sampling are susceptible to adversarial scaling attacks. View details
    Preview abstract An incentive-compatible auction incentivizes buyers to truthfully reveal their private valuations. However, many ad auction mechanisms deployed in practice are not incentive-compatible, such as first-price auctions (for display advertising) and the generalized second-price auction (for search advertising). We introduce a new metric to quantify incentive compatibility in both static and dynamic environments. Our metric is data-driven and can be computed directly through black-box auction simulations without relying on reference mechanisms or complicated optimizations. We provide interpretable characterizations of our metric and prove that it is monotone in auction parameters for several mechanisms used in practice, such as soft floors and dynamic reserve prices. We empirically evaluate our metric on ad auction data from a major ad exchange and a major search engine to demonstrate its broad applicability in practice. View details
    Robust Pricing in Dynamic Mechanism Design
    International Conference on Machine Learning (2020), pp. 2494-2503
    Preview abstract Motivated by the repeated sale of online ads via auctions, optimal pricing in repeated auctions has attracted a large body of research. While dynamic mechanisms offer powerful techniques to improve on both revenue and efficiency by optimizing auctions across different items, their reliance on exact distributional information of buyers’ valuations (present and future) limits their use in practice. In this paper, we propose robust dynamic mechanism design. We develop a new framework to design dynamic mechanisms that are robust to both estimation errors in value distributions and strategic behavior. We apply the framework in learning environments, leading to the first policy that achieves provably low regret against the optimal dynamic mechanism in contextual auctions, where the dynamic benchmark has full and accurate distributional information. View details
    Non-Clairvoyant Dynamic Mechanism Design
    Pingzhong Tang
    Econometrica, vol. 88(5) (2020), pp. 1939-1963
    Preview abstract We introduce a new family of dynamic mechanisms that restricts sellers from using future distributional knowledge. Since the allocation and pricing of each auction period do not depend on the type distributions of future periods, we call this family of dynamic mechanisms non‐clairvoyant. We develop a framework (bank account mechanisms) for characterizing, designing, and proving lower bounds for dynamic mechanisms (clairvoyant or non‐clairvoyant). We use the same methods to compare the revenue extraction power of clairvoyant and non‐clairvoyant dynamic mechanisms. View details
    Preview abstract We study fundamental graph problems such as graph connectivity, minimum spanning forest (MSF), and approximate maximum (weight) matching in a distributed setting. In particular, we focus on the Adaptive Massively Parallel Computation (AMPC) model, which is a theoretical model that captures MapReduce-like computation augmented with a distributed hash table. We show the first AMPC algorithms for all of the studied problems that run in a constant number of rounds and use only O(n^ϵ) space per machine, where 0<ϵ<1. Our results improve both upon the previous results in the AMPC model, as well as the best-known results in the MPC model, which is the theoretical model underpinning many popular distributed computation frameworks, such as MapReduce, Hadoop, Beam, Pregel and Giraph. Finally, we provide an empirical comparison of the algorithms in the MPC and AMPC models in a fault-tolerant distriubted computation environment. We empirically evaluate our algorithms on a set of large real-world graphs and show that our AMPC algorithms can achieve improvements in both running time and round-complexity over optimized MPC baselines. View details
    Optimal Dynamic Auctions are Virtual Welfare Maximizers
    Pingzhong Tang
    Proceedings of the AAAI Conference on Artificial Intelligence (2019), pp. 2125-2132
    Preview abstract We are interested in the setting where a seller sells sequentially arriving items, one per period, via a dynamic auction. At the beginning of each period, each buyer draws a private valuation for the item to be sold in that period and this valuation is independent across buyers and periods. The auction can be dynamic in the sense that the auction at period t can be conditional on the bids in that period and all previous periods, subject to certain appropriately defined incentive compatible and individually rational conditions. Perhaps not surprisingly, the revenue optimal dynamic auctions are computationally hard to find and existing literatures that aim to approximate the optimal auctions are all based on solving complex dynamic programs. It remains largely open on the structural interpretability of the optimal dynamic auctions. In this paper, we show that any optimal dynamic auction is a virtual welfare maximizer subject to some monotone allocation constraints. In particular, the explicit definition of the virtual value function above arises naturally from the primal-dual analysis by relaxing the monotone constraints. We further develop an ironing technique that gets rid of the monotone allocation constraints. Quite different from Myerson’s ironing approach, our technique is more technically involved due to the interdependence of the virtual value functions across buyers. We nevertheless show that ironing can be done approximately and efficiently, which in turn leads to a Fully Polynomial Time Approximation Scheme of the optimal dynamic auction. View details
    Preview abstract Dynamic mechanisms offer powerful techniques to improve on both revenue and efficiency by linking sequential auctions using state information, but these techniques rely on exact distributional information of the buyers’ valuations (present and future), which limits their use in learning settings. In this paper, we consider the problem of contextual auctions where the seller gradually learns a model of the buyer's valuation as a function of the context (e.g., item features) and seeks a pricing policy that optimizes revenue. Building on the concept of a bank account mechanism---a special class of dynamic mechanisms that is known to be revenue-optimal---we develop a non-clairvoyant dynamic mechanism that is robust to both estimation errors in the buyer's value distribution and strategic behavior on the part of the buyer. We then tailor its structure to achieve a policy with provably low regret against a constant approximation of the optimal dynamic mechanism in contextual auctions. Our result substantially improves on previous results that only provide revenue guarantees against static benchmarks. View details
    Dynamic Double Auctions: Towards First Best
    Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2019, San Diego, California, USA, January 6-9, 2019, pp. 157-172
    Preview abstract We study the problem of designing dynamic double auctions for two-sided markets in which a platform intermediates the trade between one seller offering independent items to multiple buyers, repeatedly over a finite horizon, when agents have private values. Motivated by online advertising and ride-hailing markets, we seek to design mechanisms satisfying the following properties: no positive transfers, i.e., the platform never asks the seller to make payments nor buyers are ever paid and periodic individual rationality, i.e., every agent should derive a non-negative utility from every trade opportunity. We provide mechanisms satisfying these requirements that are asymptotically efficient and budget-balanced with high probability as the number of trading opportunities grows. Moreover, we show that the average expected profit obtained by the platform under these mechanisms asymptotically approaches first-best (the maximum possible welfare generated by the market). View details
    Preview abstract Submodular maximization is a general optimization problem with a wide range of applications in machine learning (e.g., active learning, clustering, and feature selection). In large-scale optimization, the parallel running time of an algorithm is governed by its adaptivity, which measures the number of sequential rounds needed if the algorithm can execute polynomially-many independent oracle queries in parallel. While low adaptivity is ideal, it is not sufficient for an algorithm to be efficient in practice—there are many applications of distributed submodular optimization where the number of function evaluations becomes prohibitively expensive. Motivated by these applications, we study the adaptivity and query complexity of submodular maximization. In this paper, we give the first constant-factor approximation algorithm for maximizing a nonmonotone submodular function subject to a cardinality constraint k that runs in O(log(n)) adaptive rounds and makes O(n log(k)) oracle queries in expectation. In our empirical study, we use three real-world applications to compare our algorithm with several benchmarks for non-monotone submodular maximization. The results demonstrate that our algorithm finds competitive solutions using significantly fewer rounds and queries. View details
    Preferred Deals in General Environments
    Proceedings of the 28th International Joint Conference on Artificial Intelligence (2019), pp. 231-237
    Preview abstract A preferred deal is a special contract for selling impressions of display ad inventory. By accepting a deal, a buyer agrees to buy a minimum amount of impressions at a fixed price per impression, and is granted priority access to the impressions before they are sent to an open auction on an ad exchange. We consider the problem of designing preferred deals (inventory, price, quantity) in the presence of general convex constraints, including budget constraints, and propose an approximation algorithm to maximize the revenue obtained from the deals. We then evaluate our algorithm using auction data from a major advertising exchange and our empirical results show that the algorithm achieves around 95% of the optimal revenue. View details
    Randomized Experimental Design via Geographic Clustering
    David Rolnick
    Amir Najmi
    Proceedings of the 25th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining (2019)
    Preview abstract Web-based services often run randomized experiments to improve their products. A popular way to run these experiments is to use geographical regions as units of experimentation, since this does not require tracking of individual users or browser cookies. Since users may issue queries from multiple geographical locations, georegions cannot be considered independent and interference may be present in the experiment. In this paper, we study this problem, and first present GeoCUTS, a novel algorithm that forms geographical clusters to minimize interference while preserving balance in cluster size. We use a random sample of anonymized traffic from Google Search to form a graph representing user movements, then construct a geographically coherent clustering of the graph. Our main technical contribution is a statistical framework to measure the effectiveness of clusterings. Furthermore, we perform empirical evaluations showing that the performance of GeoCUTS is comparable to hand-crafted geo-regions with respect to both novel and existing metrics. View details
    Preview abstract Maximizing diversity is a central problem in information re- trieval and data mining systems with prominent applications in web search, recommender systems, news aggregators and product search. In this paper, we study a diversity maxi- mization problem (a.k.a. maximum dispersion problem) in which given a set of n objects in a metric space, one wants to find a subset of k objects with the maximum sum of pairwise distances. To solve this problem in a scalable distributed manner, we apply a novel distributed framework for tackling large-scale problems known as randomized composable core-sets: divide the big data set into smaller parts, solve the problem for each part, combine the solutions from each part, and solve the problem on the union of these solutions. Our algorithms improve significantly over the approximation guarantees of state-of-the-art core-set-based algorithms while using min- imum possible intermediate output size. In particular, we present a simple distributed algorithm that achieves an al- most optimal communication complexity, and moreover, it asymptotically achieves approximation factor of 1/2 which is the best possible approximation factor for the global opti- mization problem under certain complexity theory assump- tions. Our algorithms are scalable and practical as shown by our extensive empirical evaluation with large datasets and they can be easily adapted to the major distributed comput- ing systems like MapReduce. Furthermore, we show empir- ically that, in real-life instances, our algorithms reach close- to-optimal solutions with approximation factor of > 90%. This approximation factor is far exceeding the approxima- tion barrier for the problem and provide useful output. View details
    Preview abstract The Massive Parallel Computing (MPC) model gained popularity during the last decade and it is now seen as the standard model for processing large scale data. One significant shortcoming of the model is that it assumes to work on static datasets while, in practice, real world datasets evolve continuously. To overcome this issue, in this paper we initiate the study of dynamic algorithms in the MPC model. We first discuss the main requirements for a dynamic parallel model and we show how to adapt the classic MPC model to capture them. Then we analyze the connection between classic dynamic algorithms and dynamic algorithms in the MPC model. Finally, we provide new efficient dynamic MPC algorithms for a variety of fundamental graph problems, including connectivity, minimum spanning tree and matching. View details
    Preview abstract Balanced partitioning is often a crucial first step in solving large-scale graph optimization problems, e.g., in some cases, a big graph can be chopped into pieces that fit on one machine to be processed independently before stitching the results together, leading to certain suboptimality from the interaction among different pieces. In other cases, links between different parts may show up in the running time and/or network communications cost, hence the desire to have small cut size. We study a distributed balanced-partitioning problem where the goal is to partition the vertices of a given graph into k pieces so as to minimize the total cut size. Our algorithm is composed of a few steps that are easily implementable in distributed computation frameworks such as MapReduce. The algorithm first embeds nodes of the graph onto a line, and then processes nodes in a distributed manner guided by the linear embedding order. We examine various ways to find the first embedding, e.g., via a hierarchical clustering or Hilbert curves. Then we apply four different techniques including local swaps,minimum cuts on the boundaries of partitions, as well as contraction and dynamic programming. As our empirical study, we compare the above techniques with each other, and also to previous work in distributed graph algorithms, e.g., a label-propagation method [UB13], FENNEL [TGRV14] and Spinner [MLS14]. We report our results both on a private map graph and several public social networks,and show that our results beat previous distributed algorithms: For instance, compared to the label-propagation algorithm [UB13], we report an improvement of 15-25% in the cut value. We also observe that our algorithms admit scalable distributed implementation for any number of partitions. Finally, we explain three applications of this work at Google. •Balanced partitioning is used to route multi-term queries to different replicas in Google Search backend in a way that reduces the cache miss rates by≈0.5%, which leads to a double-digit gain in throughput of production clusters [AAB+19]. •Applied to the Google Maps Driving Directions, balanced partitioning minimizes the number of cross-shard queries with the goal of saving in CPU usage. This system achieves load balancing by dividing the world graph into several “shards.” Live experiments demonstrate an≈40% drop in the number of cross-shard queries when compared to a standard geography-based method. •In a job scheduling problem for our data centers, we use balanced partitioning to evenly distribute the work while minimizing the amount of communication across geographically distant servers. In fact, the hierarchical nature of our solution goes well with the layering of data center servers, where certain machines are closer to each other and have faster links to one another. View details
    Preview abstract Submodular optimization generalizes many classic problems in combinatorial optimization and has recently found a wide range of applications in machine learning (e.g., feature engineering and active learning). For many large-scale optimization problems, we are often concerned with the adaptivity complexity of an algorithm, which quantifies the number of sequential rounds where polynomially-many independent function evaluations can be executed in parallel. While low adaptivity is ideal, it is not sufficient for a distributed algorithm to be efficient, since in many practical applications of submodular optimization the number of function evaluations becomes prohibitively expensive. Motivated by these applications, we study the adaptivity and query complexity of adaptive submodular optimization. Our main result is a distributed algorithm for maximizing a monotone submodular function with cardinality constraint k that achieves a (1 − 1/e − ε)-approximation in expectation. This algorithm runs in O(log(n)) adaptive rounds and makes O(n) calls to the function evaluation oracle in expectation. The approximation guarantee and query complexity are optimal, and the adaptivity is nearly optimal. Moreover, the number of queries is substantially less than in previous works. We also extend our results to the submodular cover problem to demonstrate the generality of our algorithm and techniques. View details
    Coresets Meet EDCS: Algorithms for Matching and Vertex Cover on Massive Graphs
    Aaron Bernstein
    Cliff Stein
    Sepehr Assadi
    Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), SIAM (2019), pp. 1616-1635
    Preview abstract Maximum matching and minimum vertex cover are among the most fundamental graph optimization problems. Recently, randomized composable coresets were introduced as an effective technique for solving these problems in various models of computation on massive graphs. In this technique, one partitions the edges of an input graph randomly into multiple pieces, compresses each piece into a smaller subgraph, namely a coreset, and solves the problem on the union of these coresets to find the final solution. By designing small size randomized composable coresets, one can obtain efficient algorithms, in a black-box way, in multiple computational models including streaming, distributed communication, and the massively parallel computation (MPC) model. We develop randomized composable coresets of size Oe(n) that for any constant ε > 0, give a (3/2 + ε)-approximation to matching and a (3 + ε)-approximation to vertex cover. Our coresets improve upon the previously best approximation ratio of O(1) for matching and O(log n) for vertex cover. Most notably, our result for matching goes beyond a 2-approximation, which is a natural barrier for maximum matching in many models of computation. Our coresets lead to improved algorithms for the simultaneous communication model with randomly partitioned input, the streaming model when the input arrives in a random order, and the MPC model with O~(n√n) memory per machine and only two MPC rounds. Furthermore, inspired by the recent work of Czumaj et al. (arXiv 2017), we study algorithms for matching and vertex cover in the MPC model with only Oe(n) memory per machine. Building on our coreset constructions, we develop parallel algorithms that give an O(1)-approximation to both matching and vertex cover in only O(log log n) MPC rounds and O~(n) memory per machine. We further improve the approximation ratio of our matching algorithm to (1 + ε) for any constant ε > 0. Our results settle multiple open questions posed by Czumaj et al. A key technical ingredient of our paper is a novel application of edge degree constrained subgraphs (EDCS) that were previously introduced in the context of maintaining matchings in dynamic graphs. At the heart of our proofs are new structural properties of EDCS that identify these subgraphs as sparse certificates for large matchings and small vertex covers which are quite robust to sampling and composition. View details
    Preview abstract In modern machine learning tasks, the presence of categorical features with extremely large vocabularies is a reality. This becomes a bottleneck when using an ML model, which generally grows at least linearly with the vocabulary size, affecting the memory, training and inference costs, as well as overfitting risk. In this work, we seek to compress the vocabulary by maximizing the mutual information between the compressed categorical feature and the target binary labels. We note the relationship of this problem to that of quantization in a discrete memoryless channel, where there exists a quadratic-time algorithm to solve the problem. Unfortunately, such an algorithm does not scale to data sets with massive vocabularies and, in this paper, we develop a distributed quasi-linear O(n log n) algorithm with provable approximation guarantees. We first observe that although entropy is a submodular function, this is not the case for mutual information between a categorical feature and label. To tackle this problem, we define a set function over a different space, which still contains the optimal solution, and prove this function is submodular. We also provide a query oracle to the submodular function that runs in amortized logarithmic time, and is easy to compute in a distributed fashion. Combining these results with a greedy algorithm allows us to achieve a (1-1/e)-approximation in quasi-linear time. Finally, we compare our proposed algorithm to several existing approaches using the large-scale Criteo learning task and demonstrate better performance in retaining mutual information and also verify the learning performance of the compressed vocabulary. View details
    Variance Reduction in Bipartite Experiments through Correlation Clustering
    Warren Schudy
    Thirty-third Conference on Neural Information Processing Systems (2019) (to appear)
    Preview abstract Causal inference in randomized experiments typically assumes that the units of randomization and the units of analysis are one and the same. In some applications, however, these two roles are played by distinct entities linked by a bipartite graph. The key challenge in such bipartite settings is how to avoid interference bias, which would typically arise if we simply randomized the treatment at the level of analysis units. One effective way of minimizing interference bias in standard experiments is through cluster randomization, but this design has not been studied in the bipartite setting where conventional clustering schemes can lead to poorly powered experiments. This paper introduces a novel clustering objective and a corresponding algorithm that partitions a bipartite graph so as to maximize the statistical power of a bipartite experiment on that graph. Whereas previous work relied on balanced partitioning, our formulation suggests the use of a correlation clustering objective. We use a publicly-available graph of Amazon user-item reviews to validate our solution and illustrate how it substantially increases the statistical power in bipartite experiments. View details
    Preview abstract Motivated by the increasing need to preserve privacy in digital devices, we introduce the on-device public-private model of computation. Our motivation comes from social-network based recommender systems in which the users want to receive recommendations based on the information available on their devices, as well as the suggestions of their social contacts, without sharing such information or contacts with the central recommendation system. Our model allows us to solve many algorithmic problems while providing absolute (deterministic) guarantees of the privacy of on-device data and the user's contacts. In fact, we ensure that the private data and private contacts are never revealed to the central system. Our restrictive model of computation presents several interesting algorithmic challenges because any computation based on private information and contacts must be performed on local devices of limited capabilities. Despite these challenges, under realistic assumptions of inter-device communication, we show several efficient algorithms for fundamental data mining and machine learning problems, ranging from k-means clustering to heavy hitters. We complement this analysis with strong impossibility results for efficient private algorithms without allowing inter-device communication. In our experimental evaluation, we show that our private algorithms provide results almost as accurate as those of the non-private ones while speeding up the on-device computations by orders of magnitude. View details
    Preview abstract This paper considers a traditional problem of resource allocation, scheduling jobs on machines. One such recent application is cloud computing, where jobs arrive in an online fashion with capacity requirements and need to be immediately scheduled on physical machines in data centers. It is often observed that the requested capacities are not fully utilized, hence offering an opportunity to employ an overcommitment policy, i.e., selling resources beyond capacity. Setting the right overcommitment level can induce a significant cost reduction for the cloud provider, while only inducing a very low risk of violating capacity constraints. We introduce and study a model that quantifies the value of overcommitment by modeling the problem as a bin packing with chance constraints. We then propose an alternative formulation that transforms each chance constraint into a submodular function. We show that our model captures the risk pooling effect and can guide scheduling and overcommitment decisions. We also develop a family of online algorithms that are intuitive, easy to implement and provide a constant factor guarantee from optimal. Finally, we calibrate our model using realistic workload data, and test our approach in a practical setting. Our analysis and experiments illustrate the benefit of overcommitment in cloud services, and suggest a cost reduction of 1.5% to 17% depending on the provider's risk tolerance. View details
    Cache-aware load balancing of data center applications
    Aaron Schild
    Ray Yang
    Richard Zhuang
    Proceedings of the VLDB Endowment, vol. 12 (2019), pp. 709-723
    Preview abstract Our deployment of cache-aware load balancing in the Google web search backend reduced cache misses by ~0.5x, contributing to a double-digit percentage increase in the throughput of our serving clusters by relieving a bottleneck. This innovation has benefited all production workloads since 2015, serving billions of queries daily. A load balancer forwards each query to one of several identical serving replicas. The replica pulls each term's postings list into RAM from flash, either locally or over the network. Flash bandwidth is a critical bottleneck, motivating an application-directed RAM cache on each replica. Sending the same term reliably to the same replica would increase the chance it hits cache, and avoid polluting the other replicas' caches. However, most queries contain multiple terms and we have to send the whole query to one replica, so it is not possible to achieve a perfect partitioning of terms to replicas. We solve this via a voting scheme, whereby the load balancer conducts a weighted vote by the terms in each query, and sends the query to the winning replica. We develop a multi-stage scalable algorithm to learn these weights. We first construct a large-scale term-query graph from logs and apply a distributed balanced graph partitioning algorithm to cluster each term to a preferred replica. This yields a good but simplistic initial voting table, which we then iteratively refine via cache simulation to capture feedback effects. View details
    Preview abstract Computing approximate nearest neighbors in high dimensional spaces is a central problem in large-scale data mining with a wide range of applications in machine learning and data science. A popular and effective technique in computing nearest neighbors approximately is the Locality-Sensitive Hashing (LSH) scheme. In this paper, we aim to develop LSH schemes for distance functions that measure the distance between two probability distributions, particularly for f-divergences as well as a generalization to capture mutual information loss. First, we provide a general framework to design LHS schemes for f-divergence distance functions, and develop LSH schemes for the generalized Jensen-Shannon divergence and triangular discrimination in this framework. We show a two-sided approximation result for approximation of the generalized Jensen-Shannon divergence by the Hellinger distance, which may be of independent interest. Next, we show a general method of reducing the problem of design an LSH scheme for a Kreın kernel (which can be expressed as the difference of two positive definite kernels) to the problem of maximum inner product search. We exemplify this method by applying it to the mutual information loss divergence, due to its several important applications such as model compression. View details
    Dynamic Mechanism Design in the Field
    Rita Ren
    Proceedings of the 2018 World Wide Web Conference on World Wide Web, WWW 2018, Lyon, France, April 23-27, 2018, {ACM}, pp. 1359-1368
    Preview abstract Dynamic mechanisms are a powerful technique in designing revenue-maximizing repeated auctions. Despite their strength, these types of mechanisms have not been widely adopted in practice for several reasons, e.g., for their complexity, and for their sensitivity to the accuracy of predicting buyers' value distributions. In this paper, we aim to address these shortcomings and develop simple dynamic mechanisms that can be implemented efficiently, and provide theoretical guidelines for decreasing the sensitivity of dynamic mechanisms on prediction accuracy of buyers' value distributions. We prove that the dynamic mechanism we propose is provably dynamic incentive compatible, and introduce a notion of buyers' regret in dynamic mechanisms, and show that our mechanism achieves bounded regret while improving revenue and social welfare compared to a static reserve pricing policy. Finally, we confirm our theoretical analysis via an extensive empirical study of our dynamic auction on real data sets from online adverting. For example, we show our dynamic mechanisms can provide a 17% revenue lift with relative regret less than 0.2%. View details
    Non-Clairvoyant Dynamic Mechanism Design
    Pingzhong Tang
    Proceedings of the 2018 ACM Conference on Economics and Computation, Ithaca, NY, USA, June 18-22, 2018, ACM, pp. 169
    Preview abstract Despite their better revenue and welfare guarantees for repeated auctions, dynamic mechanisms have not been widely adopted in practice. This is partly due to the complexity of their implementation as well as their unrealistic use of forecasting for future periods. We address these shortcomings and present a new family of dynamic mechanisms that are simple and require no distributional knowledge of future periods. This paper introduces the concept of non-clairvoyance in dynamic mechanism design, which is a measure-theoretic restriction on the information that the seller is allowed to use. A dynamic mechanism is non-clairvoyant if the allocation and pricing rule at each period does not depend on the type distributions in the future periods. We develop a framework (bank account mechanisms) for characterizing, designing, and proving lower bounds for dynamic mechanisms (clairvoyant or non-clairvoyant). This framework is used to characterize the revenue extraction power of the non-clairvoyant mechanisms with respect to the mechanisms that are allowed unrestricted use of distributional knowledge. View details
    Preview abstract The k-core decomposition is a fundamental primitive in many machine learning and data mining applications. We present the first distributed and the first streaming algorithms to compute and maintain an approximate k-core decomposition with provable guarantees. Our algorithms achieve rigorous bounds on space complexity while bounding the number of passes or number of rounds of computation. We do so by presenting a new powerful sketching technique for k-core decomposition, and then by showing it can be computed efficiently in both streaming and MapReduce models. Finally, we confirm the effectiveness of our sketching technique empirically on a number of publicly available graphs. View details
    Robust Repeated Auctions Under Heterogeneous Buyer Behavior
    Shipra Agrawal
    Constantinos Daskalakis
    Proceedings of the Nineteenth ACM Conference on Economics and Computation, EC '18 (2018)
    Preview abstract We study revenue optimization in a repeated auction between a single seller and a single buyer. Traditionally, the design of repeated auctions requires strong modeling assumptions about the bidder behavior, such as it being myopic, infinite lookahead, or some specific form of learning behavior. Is it possible to design mechanisms which are simultaneously optimal against a multitude of possible buyer behaviors? We answer this question by designing a simple state-based mechanism that is simultaneously approximately optimal against a k-lookahead buyer for all k, a buyer who is a no-regret learner, and a buyer who is a policy-regret learner. Against each type of buyer our mechanism attains a constant fraction of the optimal revenue attainable against that type of buyer. We complement our positive results with almost tight impossibility results, showing that the revenue approximation tradeoffs achieved by our mechanism for different lookahead attitudes are near-optimal. View details
    Incentive-Aware Learning for Large Markets
    Proceedings of the 2018 World Wide Web Conference on World Wide Web, WWW 2018, Lyon, France, April 23-27, 2018, pp. 1369-1378
    Preview abstract In a typical learning problem, one key step is to use training data to pick one model from a collection of models that optimizes an objective function. In many multi-agent settings, the training data is generated through the actions of the agents, and the model is used to make a decision (e.g., how to sell an item) that affects the agents. An illustrative example of this is the problem of learning the reserve price in an auction. In such cases, the agents have an incentive to influence the training data (e.g., by manipulating their bids in the case of an auction) to game the system and achieve a more favorable outcome. In this paper, we study such incentive-aware learning problem in a general setting and show that it is possible to approximately optimize the objective function under two assumptions: (i) each individual agent is a “small” (part of the market); and (ii) there is a cost associated with manipulation. For our illustrative application, this nicely translates to a mechanism for setting approximately optimal reserve prices in auctions where no individual agent has significant market share. For this application, we also show that the second assumption (that manipulations are costly) is not necessary since we can “perturb” any auction to make it costly for the agents to manipulate. View details
    Preview abstract Inspired by many application of bipartite matchings in online advertising and machine learning, we study a simple and natural iterative proportional allocation algorithm: Maintain a priority score $\priority_a$ for each node $a\in\advertisers$ on one side of the bipartition, initialized as $\priority_a=1$. Iteratively allocate each node $i\in \impressions$ on the other side to eligible nodes in $\advertisers$ in proportion of their priority scores. After each round, for each node $a\in \advertisers$, decrease or increase the score $\priority_a$ based on whether it is over- or under- allocated. Our first result is that this simple, distributed algorithm converges to a $(1-\epsilon)$-approximate fractional $b$-matching solution in $O({\log n\over \epsilon^2} )$ rounds. We also extend the proportional allocation algorithm and convergence results to the maximum weighted matching problem, and show that the algorithm can be naturally tuned to produce maximum matching with {\em high entropy}. High entropy, in turn, implies additional desirable properties of this matching, e.g., it satisfies certain diversity and fairness (aka anonymity) properties that are desirable in a variety of applications in online advertising and machine learning. View details
    Stochastic bandits robust to adversarial corruptions
    Thodoris Lykouris
    Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing, STOC 2018, Los Angeles, CA, USA, June 25-29, 2018, ?114-122
    Preview abstract We introduce a new model of stochastic bandits with adversarial corruptions which aims to capture settings where most of the input follows a stochastic pattern but some fraction of it can be adversarially changed to trick the algorithm, e.g., click fraud, fake reviews and email spam. The goal of this model is to encourage the design of bandit algorithms that (i) work well in mixed adversarial and stochastic models, and (ii) whose performance deteriorates gracefully as we move from fully stochastic to fully adversarial models. We consider a setting with $K$ arms with underlying stochastic distributions such that $\Delta(a)$ is the difference between the mean of arm $a$ and the optimal arm $a^*$. The total corruption $C$ corresponds to the total perturbation that an adversary can add to the stochastic input. Our main result is an algorithm with regret bounded by {$\bigO\prn*{\sum_{a{\neq a^*}}\frac{K\cdot C\log\prn*{\nicefrac{KT}{\delta}}+\log\prn*{T}}{\Delta(a)}\cdot\log\prn*{\nicefrac{KT}{\delta}}}$ with $1-\delta$ probability and pseudoregret $\bigO\prn*{\sum_{a{\neq a^*}}\frac{K\cdot C+\log\prn*{T}}{\Delta(a)}\cdot\log\prn*{KT}}$.} Notably, our algorithm is agnostic to the total corruption and the bound holds with respect to the total corruption that was added in retrospect. We also provide a lower bound showing that the linear dependency on the corruption level is necessary. View details
    Preview abstract In the submodular welfare maximization (SWM) problem, the input consists of a set of n items, each of which must be allocated to one of m agents. Each agent ell has a valuation function v_ell, where v_ell(S) denotes the welfare obtained by this agent if she receives the set of items S. The functions v_ell are all submodular; as is standard, we assume that they are monotone and v_ell(∅) = 0. The goal is to partition the items into m disjoint subsets S1, S2, . . . , Sm in order to maximize the social welfare, defined as \Sum_ell v_ell(S_ell). A simple greedy algorithm gives a 1/2-approximation to SWM in the offline setting, and this was the best known until Vondr´ak’s recent (1 − 1/e)-approximation algorithm. In this paper, we consider the online version of SWM. Here, items arrive one at a time in an online manner; when an item arrives, the algorithm must make an irrevocable decision about which agent to assign it to before seeing any subsequent items. This problem is motivated by applications to Internet advertising, where user ad impressions must be allocated to advertisers whose value is a submodular function of the set of users/impressions they receive. There are two natural models that differ in the order in which items arrive. In the fully adversarial setting, an adversary can construct an arbitrary/worst-case instance, as well as pick the order in which items arrive in order to minimize the algorithm’s performance. In this setting, the 1/2-competitive greedy algorithm is the best possible. To improve on this, one must weaken the adversary slightly: In the random order model, the adversary can construct a worst-case set of items and valuations but does not control the order in which the items arrive; instead, they are assumed to arrive in a random order. The random order model has been well studied for online SWM and various special cases, but the best known competitive ratio (even for several special cases) is 1/2 + 1/n, which is barely better than the ratio for the adversarial order. Obtaining a competitive ratio of 1/2 + Ω(1) for the random order model has been an important open problem for several years. We solve this open problem by demonstrating that the greedy algorithm has a competitive ratio of at least 0.505 for online SWM in the random order model. This is the first result showing a competitive ratio bounded above 1/2 in the random order model, even for special cases such as the weighted matching or budgeted allocation problem (without the so-called large capacity assumptions). For special cases of submodular functions including weighted matching, weighted coverage functions, and a broader class of “second-order supermodular” functions, we provide a different analysis that gives a competitive ratio of 0.51. We analyze the greedy algorithm using a factor-revealing linear program, bounding how the assignment of one item can decrease potential welfare from assigning future items. In addition to our new competitive ratios for online SWM, we make two further contributions: First, we define the classes of second-order modular, supermodular, and submodular functions, which are likely to be of independent interest in submodular optimization. Second, we obtain an improved competitive ratio via a technique we refer to as gain linearizing, which may be useful in other contexts: Essentially, we linearize the submodular function by dividing the gain of an optimal solution into gain from individual elements, compare the algorithm’s gain when it assigns an element to the optimal solution’s gain from the element, and, crucially, bound the extent to which assigning elements can affect the potential gain of other elements. View details
    Consistent Hashing with Bounded Loads
    Mikkel Thorup
    Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms (2018), pp. 587-604
    Preview abstract Designing algorithms for balanced allocation of clients to servers in dynamic settings is a challenging problem for a variety of reasons. Both servers and clients may be added and/or removed from the system periodically, and the main objectives of allocation algorithms are: the uniformity of the allocation, and the number of moves after adding or removing a server or a client. The most popular solution for our dynamic settings is Consistent Hashing. However, the load balancing of consistent hashing is no better than a random assignment of clients to servers, so with n of each, we expect many servers to be overloaded with Θ(logn/loglogn) clients. In this paper, with n clients and n servers, we get a guaranteed max-load of 2 while only moving an expected constant number of clients for each update. We take an arbitrary user specified balancing parameter c=1+ϵ>1. With m balls and n bins in the system, we want no load above ⌈cm/n⌉. Meanwhile we want to bound the expected number of balls that have to be moved when a ball or server is added or removed. Compared with general lower bounds without capacity constraints, we show that in our algorithm when a ball or bin is inserted or deleted, the expected number of balls that have to be moved is increased only by a multiplicative factor O(1ϵ2) for ϵ≤1 (Theorem 4) and by a factor 1+O(logcc) for ϵ≥1 (Theorem 3). Technically, the latter bound is the most challenging to prove. It implies that we for superconstant c only pay a negligible cost in extra moves. We also get the same bounds for the simpler problem where we instead of a user specified balancing parameter have a fixed bin capacity C for all bins. View details
    Optimal Distributed Submodular Optimization via Sketching
    Hossein Esfandiari
    Proceedings of the 24th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (2018), pp. 1138-1147
    Preview abstract As an important special case of submodular optimization problems, coverage problems are a central problem in optimization with a wide range of applications in data mining and machine learning. As we need to handle larger and larger data sets, there is a clear need to develop distributed solutions to these problems. While several results have been developed for distributed coverage maximizations, all the existing method have notable limitations, e.g., they all achieve either suboptimal approximation guarantees or suboptimal space and memory complexities. Moreover, most previous results for submodular maximization either explicitly or implicitly assume that one has a value oracle access to the submodular function. Such a value oracle for coverage functions has the following form: given a subfamily of (input) subsets, determine the size of the union of the subsets in this subfamily. View details
    Preview abstract We study the problem of efficiently optimizing submodular functions under cardinality constraints in distributed setting. Recently, several distributed algorithms for this problem have been introduced which either achieve a sub-optimal solution or they run in super-constant number of rounds of computation. Unlike previous work, we aim to design distributed algorithms in multiple rounds with almost optimal approximation guarantees at the cost of outputting a larger number of elements. Toward this goal, we present a distributed algorithm that, for any \epsilon > 0 and any constant r, outputs a set S of O(rk/\epsilon^{1\over r}) items in r rounds, and achieves a (1-\epsilon)-approximation of the value of the optimum set with k items. This is the first distributed algorithm that achieves an approximation factor of (1-\epsilon) running in less than $\log {1\over \epsilon}$ number of rounds. We also prove a hardness result showing that the output of any $1-\epsilon$ approximation distributed algorithm limited to one distributed round should have at least $\Omega(k/\epsilon)$ items. In light of this hardness result, our distributed algorithm in one round, $r=1$, is asymptotically tight in terms of the output size. We support the theoretical guarantees with an extensive empirical study of our algorithm showing that achieving almost optimum solutions is indeed possible in a few rounds for large-scale real datasets. View details
    Almost Optimal Streaming Algorithms for Coverage Problems
    Hossein Esfandiari
    29th ACM Symposium on Parallelism in Algorithms and Architectures (2017)
    Preview abstract Maximum coverage and minimum set cover problems --collectively called coverage problems-- have been studied extensively in streaming models. However, previous research not only achieve sub-optimal approximation factors and space complexities, but also study a restricted set arrival model which makes an explicit or implicit assumption on oracle access to the sets, ignoring the complexity of reading and storing the whole set at once. In this paper, we address the above shortcomings, and present algorithms with improved approximation factor and improved space complexity, and prove that our results are almost tight. Moreover, unlike most of previous work, our results hold on a more general edge arrival model. More specifically, we present (almost) optimal approximation algorithms for maximum coverage and minimum set cover problems in the streaming model with an (almost) optimal space complexity of O~(n), i.e., the space is {\em independent of the size of the sets or the size of the ground set of elements}. These results not only improve over the best known algorithms for the set arrival model, but also are the first such algorithms for the more powerful {\em edge arrival} model. In order to achieve the above results, we introduce a new general sketching technique for coverage functions: This sketching scheme can be applied to convert an α-approximation algorithm for a coverage problem to a $(1-\eps)\alpha$-approximation algorithm for the same problem in streaming, or RAM models. We show the significance of our sketching technique by ruling out the possibility of solving coverage problems via accessing (as a black box) a $(1 \pm \eps)$-approximate oracle (e.g., a sketch function) that estimates the coverage function on any subfamily of the sets. View details
    Bicriteria Distributed Submodular Maximization in a Few Rounds
    Proceedings of the 29th ACM Symposium on Parallelism in Algorithms and Architectures (2017)
    Preview abstract We study the problem of efficiently optimizing submodular functions under cardinality constraints in distributed setting. Recently, several distributed algorithms for this problem have been introduced which either achieve a sub-optimal solution or they run in super-constant number of rounds of computation. Unlike previous work, we aim to design distributed algorithms in multiple rounds with almost optimal approximation guarantees at the cost of outputting a larger number of elements. Toward this goal, we present a distributed algorithm that, for any ε > 0 and any constant r, outputs a set S of O(rk/ε^(1/r)) items in r rounds, and achieves a (1-ε)-approximation of the value of the optimum set with k items. This is the first distributed algorithm that achieves an approximation factor of (1-ε) running in less than log 1/ε number of rounds. We also prove a hardness result showing that the output of any 1-ε approximation distributed algorithm limited to one distributed round should have at least Ω(k/ε) items. In light of this hardness result, our distributed algorithm in one round, r = 1, is asymptotically tight in terms of the output size. We support the theoretical guarantees with an extensive empirical study of our algorithm showing that achieving almost optimum solutions is indeed possible in a few rounds for large-scale real datasets. View details
    Boosted Second-price Auctions for Heterogeneous Bidders
    Negin Golrezaei
    Hamid Nazerzadeh
    Submitted for publication (2017)
    Preview abstract Due to its simplicity and desirable incentive aspects, the second-price auction is the most prevalent auction format used by advertising exchanges. However, even with the optimized choice of the reserve prices, this auction is not optimal when the bidders are heterogeneous, i.e., when the bidder valuation distributions differ significantly. We propose a new auction format called the boosted second-price auction, which favors bidders with lower inverse hazard rates (IHRs), roughly speaking, bidders with more stable bidding behavior. Based on our analysis of auction data from Google’s advertising exchange, we found bidders to be heterogeneous and can be ordered based on their IHRs. In this paper, we theoretically analyze and describe how our proposed boosted second-price auctions increase revenue over that of the widely used second-price auctions by favoring bidders with lower IHRs. We also provide practical guidelines for determining boost values and validate these guidelines both theoretically and empirically. Our counterfactuals, based on actual transaction data, show that boosted second-price auctions that follow our guidelines perform almost optimally and obtain up to 3% more revenue than second-price auctions. View details
    Affinity Clustering: Hierarchical Clustering at Scale
    Soheil Behnezhad
    Mahsa Derakhshan
    MohammadTaghi Hajiaghayi
    Raimondas Kiveris
    NIPS 2017, pp. 6867-6877
    Preview abstract Graph clustering is a fundamental task in many data-mining and machine-learning pipelines. In particular, identifying good hierarchical clustering structure is at the same time a fundamental and challenging problem for several applications. In many applications, the amount of data to analyze is increasing at an astonishing rate each day. Hence there is a need for new solutions to efficiently compute effective hierarchical clusterings on such huge data. In this paper, we propose algorithms to address this problem. First, we analyze minimum spanning tree-based clustering algorithms and their corresponding hierarchical clusterings. In particular we consider classic single-linkage clustering based on Kruskal's algorithm and a variation of Boruvka algorithm that we call affinity clustering and prove new interesting properties of these clusterings via the concept of certificates. Then we present new algorithms in the MapReduce model and their efficient real world implementations via Distributed Hash Tables (DHTs). Our MapReduce algorithms indeed improve upon the previous MapReduce algorithms for finding a minimum spanning tree in graphs as well. Finally we show experimentally that our algorithms are scalable for huge data and competitive with state-of-the-art algorithms. In particular we show that Affinity Clustering is in practice superior to several state-of-the-art clustering algorithms. View details
    A Study of Compact Reserve Pricing Languages
    Hossein Esfandiari
    Saeed Seddighin
    AAAI 2017 (2017), pp. 363-368
    Preview abstract Online advertising allows advertisers to implement fine-tuned targeting of users. While such precise targeting leads to more effective advertising, it introduces challenging multidimensional pricing and bidding problems for publishers and advertisers. In this context, advertisers and publishers need to deal with an exponential number of possibilities. As a result, designing efficient and compact multidimensional bidding and pricing systems and algorithms are practically important for online advertisement. Compact bidding languages have already been studied in the context of multiplicative bidding. In this paper, we study the compact pricing problem. View details
    Preview abstract Billions of dollars worth of display advertising are sold via contracts and deals. This paper presents a formal study of preferred deals, a new generation of contracts for selling online advertisement, that generalize the traditional reservation contracts; these contracts are suitable for advertisers with advanced targeting capabilities. We propose a constant-factor approximation algorithm for maximizing the revenue that can be obtained from these deals. We show, both theoretically and via data analysis, that deals, with appropriately chosen minimum-purchase guarantees, can yield significantly higher revenue than auctions. We evaluate our algorithm using data from Google's ad exchange platform. Our algorithm obtains about 90% of the optimal revenue where the second-price auction, even with personalized reserve, obtains at most 52% of the benchmark. View details
    Preview abstract In online advertising, advertisers purchase ad placements by participating in a long sequence of repeated auctions. One of the most important features advertising platforms often provide, and advertisers often use, is budget management, which allows advertisers to control their cumulative expenditures. Advertisers typically declare the maximum daily amount they are willing to pay, and the platform adjusts allocations and payments to guarantee that cumulative expenditures do not exceed budgets. There are multiple ways to achieve this goal, and each one, when applied to all budget-constrained advertisers simultaneously, steers the system toward a different equilibrium. While previous research focused on online stochastic optimization techniques or game-theoretic equilibria of such settings, our goal in this paper is to compare the ``system equilibria'' of a range of budget management strategies in terms of the seller's profit and buyers' utility. In particular, we consider six different budget management strategies including probabilistic throttling, thresholding, bid shading, reserve pricing, and multiplicative boosting. We show these methods admit a system equilibrium in a rather general setting, and prove dominance relations between them in a simplified setting. Our study sheds light on the impact of budget management strategies on the tradeoff between the seller's profit and buyers' utility. Finally, we also empirically compare the system equilibria of these strategies using real ad auction data in sponsored search and randomly generated bids. The empirical study confirms our theoretical findings about the relative performances of budget management strategies. View details
    Dynamic Revenue Sharing
    Advances in Neural Information Processing Systems 30: Annual Conference on Neural Information Processing Systems 2017, 4-9 December 2017, Long Beach, CA, USA
    Preview abstract Many online platforms act as intermediaries between a seller and a set of buyers. Examples of such settings include online retailers (such as Ebay) selling items on behalf of sellers to buyers, or advertising exchanges (such as AdX) selling pageviews on behalf of publishers to advertisers. In such settings, revenue sharing is a central part of running such a marketplace for the intermediary, and fixed-percentage revenue sharing schemes are often used to split the revenue among the platform and the sellers. In particular, such revenue sharing schemes require the platform to (i) take at most a constant fraction α of the revenue from auctions and (ii) pay the seller at least the seller declared opportunity cost c for each item sold. A straightforward way to satisfy the constraints is to set a reserve price at c/(1 − α ) for each item, but it is not the optimal solution on maximizing the profit of the intermediary. While previous studies (by Mirrokni and Gomes, and by Niazadeh et al) focused on revenue-sharing schemes in static double auctions, in this paper, we take advantage of the repeated nature of the auctions, and present solutions based on dynamic mechanism design. In particular, we introduce dynamic revenue sharing schemes where we balance the two constraints over different auctions to achieve higher profit. This is directly motivated by the practice of advertising exchanges where the fixed-percentage revenue-share should be met across all auctions and not in each auction. In this paper, we characterize the optimal revenue sharing scheme that satisfies both constraints in expectation. Finally, we empirically evaluate our revenue sharing scheme on real data. View details
    Preview abstract Feature selection is a fundamental problem in machine learning and data mining. The majority of feature selection algorithms are designed for running on a single machine (centralized setting) and they are less applicable to very large datasets. Although there are some distributed methods to tackle this problem, most of them are distributing the data horizontally which are not suitable for datasets with a large number of features and few number of instances. Thus, in this paper, we introduce a novel vertically distributable feature selection method in order to speed up this process and be able to handle very large datasets in a scalable manner. In general, feature selection methods aim at selecting relevant and non-redundant features (Minimum Redundancy and Maximum Relevance). It is much harder to consider redundancy in a vertically distributed setting than a centralized setting since there is no global access to the whole data. To the best of our knowledge, this is the first attempt toward solving the feature selection problem with a vertically distributed filter method which handles the redundancy with consistently comparable results with centralized methods. In this paper, we formalize the feature selection problem as a diversity maximization problem by introducing a mutual-information-based metric distance on the features. We show the effectiveness of our method by performing an extensive empirical study. In particular, we show that our distributed method outperforms state-of-the-art centralized feature selection algorithms on a variety of datasets. From a theoretical point of view, we have proved that the used greedy algorithm in our method achieves an approximation factor of 1/4 for the diversity maximization problem in a distributed setting with high probability. Furthermore, we improve this to 8/25 expected approximation using multiplicity in our distribution. View details
    A study of compact reserve pricing languages
    Hossein Esfandiari
    Saeed Seddighin
    Proceedings of the Thirty-First AAAI Conference on Artificial Intelligence (2017), pp. 363-368
    Preview abstract Motivated by ad auctions we study the multiplicative reserve price system (MRPS). MRPS is a compact way to set reserve prices on several auctions simultaneously. In this paper first we consider the problem of finding the best way of assigning reserve prices in this system. We show that this problem is NP-hard. Next, by characterizing the the properties of an optimum solution we design an approximation algorithm for this problem. Interestingly, our experiments show that our algorithm achieves 90–98% of the optimum solution that sets the reserve price of each auction independently (i.e., the optimum set of reserve prices). We show that in the adversarial setting we lose at most a logarithmic factor compare to the optimum set of reserve prices. To show the tightness of our results in the adversarial setting, we show that there is no compact pricing system (i.e. a pricing system that uses O(n^{1−ε}) bits to set n reserve prices) that loses less than a logarithmic factor compare to the optimum set of reserve prices, in the worst case. Notice that, interestingly, this hardness result holds for any pricing system and not only MRPS. View details
    Preview abstract We study the dynamic mechanism design problem of a seller who repeatedly sells independent items to a buyer with private values. In this setting, the seller could potentially extract the entire buyer surplus by running efficient auctions and charging an upfront participation fee at the beginning of the horizon. In some markets, such as internet advertising, participation fees are not practical since buyers expect to inspect items before purchasing them. This motivates us to study the design of dynamic mechanisms under successively more stringent requirements that capture the implicit business constraints of these markets. We first consider a periodic individual rationality constraint, which limits the mechanism to charge at most the buyer's value in each period. While this prevents large upfront participation fees, the seller can still design mechanisms that spread a participation fee across the first few auctions. These mechanisms have the unappealing feature that they provide close-to-zero buyer utility in the first auctions in exchange for higher utility in future auctions. To address this problem, we introduce a martingale utility constraint, which imposes the requirement that from the perspective of the buyer, the next item's expected utility is equal to the present one's. Our main result is providing a dynamic auction satisfying martingale utility and periodic individual rationality whose profit loss with respect to first-best (full extraction of buyer surplus) is optimal up to polylogarithmic factors. The proposed mechanism is a dynamic two-tier auction with a hard floor and a soft floor that allocates the item whenever the buyer's bid is above the hard floor and charges the minimum of the bid and the soft floor. View details
    Overcommitment in Cloud Services – Bin Packing with Chance Constraints
    Maxime Cohen
    Phil Keller
    ACM SIGMETRICS / International Conference on Measurement and Modeling of Computer Systems 2017
    Preview abstract This paper considers the traditional problem of resource allocation, i.e., scheduling jobs on machines. One such recent application is cloud computing, where jobs arrive in an online fashion with capacity requirements and need to be allocated to physical machines. It is often observed that the requested capacities are not fully utilized, hence offering an opportunity to employ an overcommitment policy, i.e., selling resources beyond capacity. Setting the right overcommitment level can induce a significant cost reduction for the cloud provider, while taking a very low risk of violating capacity constraints. We introduce and study a model that quantifies the value of overcommitment by modeling the problem as a bin packing with chance constraints. We then propose an alternative formulation that transforms each chance constraint into a sub-modular function. We show that our model captures the risk pooling effect and allows to guide scheduling and overcommitment decisions. We also develop a family of online algorithms that are intuitive, easy to implement and provide a constant factor guarantee from optimal. Finally, we calibrate our model using realistic workload data and test our approach in a practical setting. Our analysis and experiments illustrate the benefit of overcommitting in cloud services. View details
    Preview abstract Online allocation problems have been widely studied due to their numerous practical applications (particularly to Internet advertising), as well as considerable theoretical interest. The main challenge in such problems is making assignment decisions in the face of uncertainty about future input; effective algorithms need to predict which constraints are most likely to bind, and learn the balance between short-term gain and the value of long-term resource availability. In many important applications, the algorithm designer is faced with multiple objectives to optimize. In particular, in online advertising it is fairly common to optimize multiple metrics, such as clicks, conversions, and impressions, as well as other metrics which may be largely uncorrelated such as ‘share of voice’, and ‘buyer surplus’. While there has been considerable work on multi-objective offline optimization (when the entire input is known in advance), very little is known about the online case, particularly in the case of adversarial input. In this paper, we give the first results for bi-objective online submodular optimization, providing almost matching upper and lower bounds for allocating items to agents with two submodular value functions. We also study practically relevant special cases of this problem related to Internet advertising, and obtain improved results. All our algorithms are nearly best possible, as well as being efficient and easy to implement in practice. View details
    Expander via Local Edge Flips
    Zeyuan Allen-Zhu
    Aditya Bhaskara
    Lorenzo Orecchia
    SODA (2016)
    Preview abstract Designing distributed and scalable algorithms to improve network connectivity is a central topic in peer-to-peer networks. In this paper we focus on the following well-known problem: given an n-node d-regular network for d = Ω(log n), we want to design a decentralized, local algorithm that transforms the graph into one that has good connectivity properties (low diameter, expansion, etc.) without affecting the sparsity of the graph. To this end, Mahlmann and Schindelhauer introduced the random "flip" transformation, where in each time step, a random pair of vertices that have an edge decide to 'swap a neighbor'. They conjectured that performing O(nd) such flips at random would convert any connected d-regular graph into a d-regular expander graph, with high probability. However, the best known upper bound for the number of steps is roughly O(n17d23), obtained via a delicate Markov chain comparison argument. Our main result is to prove that a natural instantiation of the random flip produces an expander in at most O(n2d2[EQUATION] n) steps, with high probability. Our argument uses a potential-function analysis based on the matrix exponential, together with the recent beautiful results on the higher-order Cheeger inequality of graphs. We also show that our technique can be used to analyze another well-studied random process known as the 'random switch', and show that it produces an expander in O(nd) steps with high probability. View details
    Distributed Balanced Partitioning via Linear Embedding
    Ninth ACM International Conference on Web Search and Data Mining (WSDM), ACM (2016), pp. 387-396
    Preview abstract Balanced partitioning is often a crucial first step in solving large-scale graph optimization problems: in some cases, a big graph is chopped into pieces that fit on one machine to be processed independently before stitching the results together, leading to certain suboptimality from the interaction among different pieces. In other cases, links between different parts may show up in the running time and/or network communications cost, hence the desire to have small cut size. We study a distributed balanced partitioning problem where the goal is to partition the vertices of a given graph into k pieces, minimizing the total cut size. Our algorithm is composed of a few steps that are easily implementable in distributed computation frameworks, e.g., MapReduce. The algorithm first embeds nodes of the graph onto a line, and then processes nodes in a distributed manner guided by the linear embedding order. We examine various ways to find the first embedding, e.g., via a hierarchical clustering or Hilbert curves. Then we apply four different techniques such as local swaps, minimum cuts on partition boundaries, as well as contraction and dynamic programming. Our empirical study compares the above techniques with each other, and to previous work in distributed algorithms, e.g., a label propagation method [34], FENNEL [32] and Spinner [23]. We report our results both on a private map graph and several public social networks, and show that our results beat previous distributed algorithms: we notice, e.g., 15-25% reduction in cut size over [34]. We also observe that our algorithms allow for scalable distributed implementation for any number of partitions. Finally, we apply our techniques for the Google Maps Driving Directions to minimize the number of multi-shard queries with the goal of saving in CPU usage. During live experiments, we observe an ≈ 40% drop in the number of multi-shard queries when comparing our method with a standard geography-based method. View details
    Preview abstract Coverage problems are central in optimization and have a wide range of applications in data mining and machine learning. While several distributed algorithms have been developed for coverage problems, the existing methods suffer from several limitations, e.g., they all achieve either suboptimal approximation guarantees or suboptimal space and memory complexities. In addition, previous algorithms developed for submodular maximization assume oracle access, and ignore the computational complexity of communicating large subsets or computing the size of the union of the subsets in this subfamily. In this paper, we develop an improved distributed algorithm for the k-cover and the set cover with λ outliers problems, with almost optimal approximation guarantees, almost optimal memory complexity, and linear communication complexity running in only four rounds of computation. Finally, we perform an extensive empirical study of our algorithms on a number of publicly available real data sets, and show that using sketches of size 30 to 600 times smaller than the input, one can solve the coverage maximization problem with quality very close to that of the state-of-the-art single-machine algorithm. View details
    Dynamic Auctions with Bank Accounts
    Pingzhong Tang
    Proceedings of the Twenty-Fifth International Joint Conference on Artificial Intelligence (2016), pp. 387-393
    Preview abstract Consider a buyer with independent additive valuations for a set of goods, and a seller who is constrained to sell one item at a time in an online fashion. If the seller is constrained to run independent auctions for each item, then he would run Myerson’s optimal auction for each item. If the seller is allowed to use the full power of dynamic mechanism design and have the auction for each item depend on the outcome of the previous auctions, he is able to perform much better. The main issues in implementing such strategies in online settings where items arrive over time are that the auction might be too complicated or it makes too strong assumptions on the buyer’s rationality or seller’s commitment over time. This motivates us to explore a restricted family of dynamic auctions that can be implemented in an online fashion and without too much commitment from the seller ahead of time. In particular, we study a set of auction in which the space of single-shot auctions is augmented with a structure that we call bank account, a real number for each node that summarizes the history so far. This structure allows the seller to store deficits or surpluses of buyer utility from each individual auction and even them out on the long run. This is akin to enforcing individual rationality constraint on average rather than per auction. We also study the effect of enforcing a maximum limit to the values that bank account might grow, which means that we enforce that besides the auction being individually rational on average it is also not far from being individually rational at any given interval. Interestingly, even with these restrictions, we can achieve significantly better revenue and social welfare compared to separate Myerson auctions. View details
    Linear Relaxations for Finding Diverse Elements in Metric Spaces
    Aditya Bhaskara
    Mehrdad Ghadiri
    Ola Svensson
    NIPS (2016), pp. 4098-4106
    Preview abstract Choosing a diverse subset of a large collection of points in a metric space is a fundamental problem, with applications in feature selection, recommender systems, web search, data summarization, etc. Various notions of diversity have been proposed, tailored to different applications. The general algorithmic goal is to find a subset of points that maximize diversity, while obeying a cardinality (or more generally, matroid) constraint. The goal of this paper is to develop a novel linear programming (LP) framework that allows us to design approximation algorithms for such problems. We study an objective known as sum-min diversity, which is known to be effective in many applications, and give the first constant factor approximation algorithm. Our LP framework allows us to easily incorporate additional constraints, as well as secondary objectives. We also prove a hardness result for two natural diversity objectives, under the so-called planted clique assumption. Finally, we study the empirical performance of our algorithm on several standard datasets. We first study the approximation quality of the algorithm by comparing with the LP objective. Then, we compare the quality of the solutions produced by our method with other popular diversity maximization algorithms. View details
    Preview abstract In the context of online ad serving, display ads may appear on different types of webpages, where each page includes several ad slots and therefore multiple ads can be shown on each page. The set of ads that can be assigned to ad slots of the same page needs to satisfy various prespecified constraints including exclusion constraints, diversity constraints, and the like. Upon arrival of a user, the ad serving system needs to allocate a set of ads to the current webpage respecting these per-page allocation constraints. Previous slot-based settings ignore the important concept of a page and may lead to highly suboptimal results in general. In this article, motivated by these applications in display advertising and inspired by the submodular welfare maximization problem with online bidders, we study a general class of page-based ad allocation problems, present the first (tight) constant-factor approximation algorithms for these problems, and confirm the performance of our algorithms experimentally on real-world datasets. A key technical ingredient of our results is a novel primal-dual analysis for handling free disposal, which updates dual variables using a “level function” instead of a single level and unifies with previous analyses of related problems. This new analysis method allows us to handle arbitrarily complicated allocation constraints for each page. Our main result is an algorithm that achieves a 1 &minus frac 1 e &minus o(1)-competitive ratio. Moreover, our experiments on real-world datasets show significant improvements of our page-based algorithms compared to the slot-based algorithms. Finally, we observe that our problem is closely related to the submodular welfare maximization (SWM) problem. In particular, we introduce a variant of the SWM problem with online bidders and show how to solve this problem using our algorithm for whole-page optimization. View details
    Preview abstract The problem of matrix column subset selection has recently attracted a large body of research, with feature selection serving as one obvious and important application. Among the techniques that have been applied to solve this problem, the greedy algorithm has been shown to be quite effective in practice. However, our theoretical guarantees on its performance have not been ex- plored thoroughly, especially in a distributed set- ting. In this paper, we study the greedy algorithm for the column subset selection problem from a theoretical and empirical perspective and show its effectiveness in a distributed setting. In par- ticular, we provide an improved approximation guarantee for the greedy algorithm, and present the first distributed implementation of this algo- rithm with provable approximation factors. We use the idea of randomized composable core- sets, developed recently in the context of sub- modular maximization. Finally, we validate the effectiveness of this distributed algorithm via an empirical study. View details
    Preview abstract Despite their better revenue and welfare guarantees for repeated auctions, dynamic mechanisms have not been widely adopted in practice. This is partly due to their computational and implementation complexity, and also due to their unrealistic use of forecasting for future periods. We address the above shortcomings and present a new family of dynamic mechanisms that are computationally efficient and do not use any distribution knowledge of future periods. Our contributions are three-fold: 1. We present the first polynomial-time dynamic incentive-compatible and ex-post individually rational mechanism for multiple periods and for any number of buyers that is a constant approximation to the optimal revenue. Unlike previous mechanisms, we require no expensive pre-processing step and in each period we run a simple auction that is a combination of virtual value maximizing auctions. 2. We introduce the concept of obliviousness in dynamic mechanism design. A dynamic mechanism is oblivious if the allocation and pricing rule at each period does not depend on the type distributions in future periods. Our mechanism is oblivious and guarantees a 5-approximation compared to the optimal mechanism that knows all the distributions in advance. 3. We develop a framework for characterizing, designing, and proving lower bounds for dynamic mechanisms (oblivious or not). In addition to the aforementioned positive results, we use this characterization to show that no oblivious mechanism can produce a better-than-2 approximation to the mechanism that knows all the distributions. View details
    Preview abstract In this paper, we present a study of the community structure of ego-networks—the graphs representing the connections among the neighbors of a node—for several online social networks. Toward this goal, we design a new technique to efficiently build and cluster all the ego-nets of a graph in parallel (note that even just building the ego-nets efficiently is challenging on large networks). Our experimental findings are quite compelling: at a microscopic level it is easy to detect high quality communities. Leveraging on this fact we, then, develop new features for friend suggestion based on co-occurrences of two nodes in different ego-nets’ communities. Our new features can be computed efficiently on very large scale graphs by just analyzing the neighborhood of each node. Furthermore, we prove formally on a stylized model, and by experimental analysis that this new similarity measure outperforms the classic local features employed for friend suggestions View details
    Preview abstract We consider the setting where a seller must allocate a collection of goods to budgeted buyers, as exemplified by online advertising systems where platforms decide which impressions to serve to various advertisers. Such resource allocation problems are challenging for two reasons: (a) the seller must strike a balance between optimizing her own revenues and guaranteeing fairness to her (repeat) buyers and (b) the problem is inherently dynamic due to the uncertain, time-varying supply of goods available with the seller. We propose a stochastic approximation scheme akin to a dynamic market equilibrium. Our scheme relies on frequent re-solves of an Eisenberg-Gale convex program, and does not require the seller to have any knowledge about how goods arrival processes evolve over time. The scheme fully extracts buyer budgets (thus maximizing seller revenues), while at the same time provides a 0.47 approximation of the proportionally fair allocation of goods achievable in the offline case, as long as the supply of goods comes from a wide family of (possibly non-stationary) Gaussian processes. We then extend our results to a more general family of metrics called \alpha-fairness. Finally, we deal with a multi-objective problem where the seller is concerned with both the proportional fairness and efficiency of the allocation, and propose a hybrid algorithm which achieves a 0.27 bi-criteria guarantee against fairness and efficiency. View details
    Reservation Exchange Markets for Internet Advertising
    Gagan Goel
    Stefano Leonardi
    Afshin Nikzad
    LIPIcs, vol. 55, 142:1-142:13
    Preview abstract Internet display advertising industry follows two main business models. One model is based on direct deals between publishers and advertisers where they sign legal contracts containing terms of fulfillment for a future inventory. The second model is a spot market based on auctioning page views in real-time on advertising exchange (AdX) platforms such as DoubleClick's Ad Exchange, RightMedia, or AppNexus. These exchanges play the role of intermediaries who sell items (e.g. page-views) on behalf of a seller (e.g. a publisher) to buyers (e.g., advertisers) on the opposite side of the market. The computational and economics issues arising in this second model have been extensively investigated in recent times. In this work, we consider a third emerging model called reservation exchange market. A reservation exchange is a two-sided market between buyer orders for blocks of advertisers' impressions and seller orders for blocks of publishers' page views. The goal is to match seller orders to buyer orders while providing the right incentives to both sides. In this work we first describe the important features of mechanisms for efficient reservation exchange markets. We then address the algorithmic problems of designing revenue sharing schemes to provide a fair division between sellers of the revenue collected from buyers. A major conceptual contribution of this work is in showing that even though both clinching ascending auctions and VCG mechanisms achieve the same outcome from a buyer perspective, however, from the perspective of revenue sharing among sellers, clinching ascending auctions are much more informative than VCG auctions. View details
    Preview abstract An effective technique for solving optimization problems over massive data sets is to partition the data into smaller pieces, solve the problem on each piece and compute a representative solution from it, and finally obtain a solution inside the union of the representative solutions for all pieces. This technique can be captured via the concept of composable core-sets, and has been recently applied to solve diversity maximization problems as well as several clustering problems [7,15,8]. However, for coverage and submodular maximization problems, impossibility bounds are known for this technique [15]. In this paper, we focus on efficient construction of a randomized variant of composable core-sets where the above idea is applied on a random clustering of the data. We employ this technique for the coverage, monotone and non-monotone submodular maximization problems. Our results significantly improve upon the hardness results for non-randomized core-sets, and imply improved results for submodular maximization in a distributed and streaming settings. The effectiveness of this technique has been confirmed empirically for several machine learning applications [22], and our proof provides a theoretical foundation to this idea. In summary, we show that a simple greedy algorithm results in a 1/3-approximate randomized composable core-set for submodular maximization under a cardinality constraint. Our result also extends to non-monotone submodular functions, and leads to the first 2-round MapReduce-based constant-factor approximation algorithm with O(n) total communication complexity for either monotone or non-monotone functions. Finally, using an improved analysis technique and a new algorithm PseudoGreedy, we present an improved 0.545-approximation algorithm for monotone submodular maximization, which is in turn the first MapReduce-based algorithm beating factor 1/2 in a constant number of rounds. View details
    Automated Decomposition of Build Targets
    Mohsen Vakilian
    J. David Morgenthaler
    Proceedings of the 37th International Conference on Software Engineering, IEEE Computer Society (2015), pp. 123-133
    Preview abstract A (build) target specifies the information that is needed to automatically build a software artifact. This paper focuses on underutilized targets—an important dependency problem that we identified at Google. An underutilized target is one with files not needed by some of its dependents. Underutilized targets result in less modular code, overly large artifacts, slow builds, and unnecessary build and test triggers. To mitigate these problems, programmers decompose underutilized targets into smaller targets. However, manually decomposing a target is tedious and error-prone. Although we prove that finding the best target decomposition is NP-hard, we introduce a greedy algorithm that proposes a decomposition through iterative unification of the strongly connected components of the target. Our tool found that 19,994 of 40,000 Java library targets at Google can be decomposed to at least two targets. The results show that our tool is (1) efficient because it analyzes a target in two minutes on average and (2) effective because for each of 1,010 targets, it would save at least 50% of the total execution time of the tests triggered by the target. View details
    Preview abstract As a fundamental tool in modeling and analyzing social, and information networks, large-scale graph mining is an important component of any tool set for big data analysis. Processing graphs with hundreds of billions of edges is only possible via developing distributed algorithms under distributed graph mining frameworks such as MapReduce, Pregel, Gigraph, and alike. For these distributed algorithms to work well in practice, we need to take into account several metrics such as the number of rounds of computation and the communication complexity of each round. For example, given the popularity and ease-of-use of MapReduce framework, developing practical algorithms with good theoretical guarantees for basic graph algorithms is a problem of great importance. In this tutorial, we first discuss how to design and implement algorithms based on traditional MapReduce architecture. In this regard, we discuss various basic graph theoretic problems such as computing connected components, maximum matching, MST, counting triangle and overlapping or balanced clustering. We discuss a computation model for MapReduce and describe the sampling, filtering, local random walk, and core-set techniques to develop efficient algorithms in this framework. At the end, we explore the possibility of employing other distributed graph processing frameworks. In particular, we study the effect of augmenting MapReduce with a distributed hash table (DHT) service and also discuss the use of a new graph processing framework called ASYMP based on asynchronous message-passing method. In particular, we will show that using ASyMP, one can improve the CPU usage, and achieve significantly improved running time. View details
    Expanders via Local Edge Flips
    Zeyuan Allen-Zhu,
    Aditya Bhaskara
    Lorenzo Orecchia
    Society for Industrial and Applied Mathematics (2015), pp. 259-269
    Preview abstract Designing distributed and scalable algorithms to improve network connectivity is a central topic in peer-to-peer networks. In this paper we focus on the following well-known problem: given an n-node d-regular network for d=Ω(logn), we want to design a decentralized, local algorithm that transforms the graph into one that has good connectivity properties (low diameter, expansion, etc.) without affecting the sparsity of the graph. To this end, Mahlmann and Schindelhauer introduced the random "flip" transformation, where in each time step, a random pair of vertices that have an edge decide to `swap a neighbor'. They conjectured that performing O(nd) such flips at random would convert any connected d-regular graph into a d-regular expander graph, with high probability. However, the best known upper bound for the number of steps is roughly O(n^17d^23), obtained via a delicate Markov chain comparison argument. Our main result is to prove that a natural instantiation of the random flip produces an expander in at most O(n^2d^2√logn) steps, with high probability. Our argument uses a potential-function analysis based on the matrix exponential, together with the recent beautiful results on the higher-order Cheeger inequality of graphs. We also show that our technique can be used to analyze another well-studied random process known as the `random switch', and show that it produces an expander in O(nd) steps with high probability. View details
    Dynamic Coordination Mechanisms
    Janardhan Kulkarni
    SIGMETRICS Performance Evaluation Review (2015), pp. 77
    Preview abstract Handling the lack of coordination while designing efficient algorithms in distributed systems has been a major topic of study in the past decade. Coordination mechanisms have been proposed as a tool to deal with the issue as well as lack of access to global information in settings such as distributed systems. In the context of resource allocation, a coordination mechanism is a set of local policies that assigns a cost to each strategy based on the available local information. For example, in machine scheduling, this cost only depends on the processing times of jobs assigned to the same machine. Although a great tool to study distributed algorithms in the presence of self-interested agents, coordination mechanisms have few deficiencies as an analysis tool for distributed game theoretic environments. For example, in many real-world settings, we do not know the exact processing time of a job before it finishes. Furthermore, in many settings, jobs arrive online, and have different release times. Motivated by these requirements, we propose dynamic coordination mechanisms, in which each job selects a machine by looking at the set of jobs currently on each machine and it can change its decision over time. In other words, jobs can dynamically choose the (best machine dynamically. We study scheduling and resource allocation problems in this framework. Here, we are given a set of M machines and a set N of jobs or players. Each job j ∈ N has pj units of processing requirement. The mechanism designer, however, is not aware of the processing lengths of jobs. This is commonly referred to as non-clairvoyant setting in the machine scheduling literature. We consider two machine models: In the related machine model, each machine has a speed νi, and a job can choose any machine i ∈ M. In the restricted assignment model, every machine has same speed; however, a job j can only go to a subset of machines Mj . View details
    Decentralized utilitarian mechanisms for scheduling games
    Richard Cole
    José R. Correa
    Vasilis Gkatzelis
    Neil Olver
    Games and Economic Behavior, vol. 92 (2015), pp. 306-326
    Preview abstract Game Theory and Mechanism Design are by now standard tools for studying and designing massive decentralized systems. Unfortunately, designing mechanisms that induce socially efficient outcomes often requires full information and prohibitively large computational resources. In this work we study simple mechanisms that require only local information. Specifically, in the setting of a classic scheduling problem, we demonstrate local mechanisms that induce outcomes with social cost close to that of the socially optimal solution. Somewhat counter-intuitively, we find that mechanisms yielding Pareto dominated outcomes may in fact enhance the overall performance of the system, and we provide a justification of these results by interpreting these inefficiencies as externalities being internalized. We also show how to employ randomization to obtain yet further improvements. Lastly, we use the game-theoretic insights gained to obtain a new combinatorial approximation algorithm for the underlying optimization problem. Decentralized utilitarian mechanisms for scheduling games. Available from: https://www.researchgate.net/publication/275166819_Decentralized_utilitarian_mechanisms_for_scheduling_games [accessed May 2, 2017]. View details
    Preview abstract We introduce the public-private model of graphs. In this model, we have a public graph and each node in the public graph has an associated private graph. The motivation for studying this model stems from social networks, where the nodes are the users, the public graph is visible to everyone, and the private graph at each node is visible only to the user at the node. From each node's viewpoint, the graph is just a union of its private graph and the public graph. We consider the problem of efficiently computing various properties of the graphs from each node's point of view, with minimal amount of recomputation on the public graph. To illustrate the richness of our model, we explore two powerful computational paradigms for studying large graphs, namely, sketching and sampling, and focus on some key problems in social networks and show efficient algorithms in the public-private graph model. In the sketching model, we show how to efficiently approximate the neighborhood function, which in turn can be used to approximate various notions of centrality. In the sampling model, we focus on all-pair shortest path distances, node similarities, and correlation clustering. View details
    Preview abstract Motivated by Internet advertising applications, online allocation problems have been studied extensively in various adversarial and stochastic models. While the adversarial arrival models are too pessimistic, many of the stochastic (such as i.i.d or random-order) arrival models do not realistically capture uncertainty in predictions. A significant cause for such uncertainty is the presence of unpredictable traffic spikes, often due to breaking news or similar events. To address this issue, a simultaneous approximation framework has been proposed to develop algorithms that work well both in the adversarial and stochastic models; however, this framework does not enable algorithms that make good use of partially accurate forecasts when making online decisions. In this paper, we propose a robust online stochastic model that captures the nature of traffic spikes in online advertising. In our model, in addition to the stochastic input for which we have good forecasting, an unknown number of impressions arrive that are adversarially chosen.We design algorithms that combine an stochastic algorithm with an online algorithm that adaptively reacts to inaccurate predictions. We provide provable bounds for our new algorithms in this framework. We accompany our positive results with a set of hardness results showing that that our algorithms are not far from optimal in this framework. As a byproduct of our results, we also present improved online algorithms for a slight variant of the simultaneous approximation framework. View details
    Preview abstract Display advertising is the major source of revenue for service and content providers on the Internet. Here, the authors explain the prevalent mechanisms for selling display advertising, including reservation contracts and real-time bidding. Discussing some of the important challenges in this market from optimization and economic perspectives, they also survey recent results and directions for future research. View details
    Preview abstract In the Submodular Welfare Maximization (SWM) problem, the input consists of a set of n items, each of which must be allocated to one of m agents. Each agent l has a valuation function vl, where vl(S) denotes the welfare obtained by this agent if she receives the set of items S. The functions vl are all submodular; as is standard, we assume that they are monotone and vl(∅) = 0. The goal is to partition the items into m disjoint subsets S1, S2, ... Sm in order to maximize the social welfare, defined as ∑l = 1m vl(Sl). A simple greedy algorithm gives a 1/2-approximation to SWM in the offline setting, and this was the best known until Vondrak's recent (1-1/e)-approximation algorithm [34]. In this paper, we consider the online version of SWM. Here, items arrive one at a time in an online manner; when an item arrives, the algorithm must make an irrevocable decision about which agent to assign it to before seeing any subsequent items. This problem is motivated by applications to Internet advertising, where user ad impressions must be allocated to advertisers whose value is a submodular function of the set of users / impressions they receive. There are two natural models that differ in the order in which items arrive. In the fully adversarial setting, an adversary can construct an arbitrary / worst-case instance, as well as pick the order in which items arrive in order to minimize the algorithm's performance. In this setting, the 1/2-competitive greedy algorithm is the best possible. To improve on this, one must weaken the adversary slightly: In the random order model, the adversary can construct a worst-case set of items and valuations, but does not control the order in which the items arrive; instead, they are assumed to arrive in a random order. The random order model has been well studied for online SWM and various special cases, but the best known competitive ratio (even for several special cases) is 1/2 + 1/n [9,10], barely better than the ratio for the adversarial order. Obtaining a competitive ratio of 1/2 + Ω(1) for the random order model has been an important open problem for several years. We solve this open problem by demonstrating that the greedy algorithm has a competitive ratio of at least 0.505 for online SWM in the random order model. This is the first result showing a competitive ratio bounded above 1/2 in the random order model, even for special cases such as the weighted matching or budgeted allocation problems (without the so-called 'large capacity' assumptions). For special cases of submodular functions including weighted matching, weighted coverage functions and a broader class of "second-order supermodular" functions, we provide a different analysis that gives a competitive ratio of 0.51. We analyze the greedy algorithm using a factor-revealing linear program, bounding how the assignment of one item can decrease potential welfare from assigning future items. We also formulate a natural conjecture which, if true, would improve the competitive ratio of the greedy algorithm to at least 0.567. In addition to our new competitive ratios for online SWM, we make two further contributions: First, we define the classes of second-order modular, supermodular, and submodular functions, which are likely to be of independent interest in submodular optimization. Second, we obtain an improved competitive ratio via a technique we refer to as gain linearizing, which may be useful in other contexts (see [26]): Essentially, we linearize the submodular function by dividing the gain of an optimal solution into gain from individual elements, compare the gain when it assigns an element to the optimal solution's gain from the element, and, crucially, bound the extent to which assigning elements can affect the potential gain of other elements. View details
    Optimal Coordination Mechanisms for Unrelated Machine Scheduling
    Yossi Azar
    Lisa Fleischer
    Kamal Jain
    Operations Research, vol. 63 (2015), pp. 489-500
    Preview
    Preview abstract Bounding the price of anarchy (PoA), which quantifies the degradation in the quality of outcomes in a (pure) Nash equilibrium of a game, is one of the fundamental questions in computational game theory. However, for a large class of games, a pure NE may not always exist and hence a natural question to pursue is to quantify the inefficiency for weaker notions of equilibrium such as mixed Nash equilibrium, correlated equilibrium or coarse correlated equilibrium, all of which are known to exist for finite games. Several techniques have been developed for bounding the price of anarchy, yet, only a handful of them are applicable for proving the PoA bounds for general equilibrium concepts. Most notable among such techniques is Roughgarden's elegant smoothness framework, which led to the concept of robust price of anarchy. The term refers to the inefficiency bounds applicable to general equilibrium notions such as coarse correlated equilibrium. In this paper, we develop a new framework based on LP and Fenchel duality for bounding the robust price of anarchy for a large class of games. We use our framework to give the first PoA bounds for temporal routing games on graphs and energy minimization games in machine scheduling. Most notably, we present the first coordination mechanisms with bounded PoA for temporal routing over general graphs, show a related lowerbound result, and an improved bound on the price of stability for this game. Previously, coordination mechanisms with bounded PoA were only known for restricted classes of graphs such as trees or parallel edges. Furthermore, we demonstrate the wide applicability of our framework by giving new proofs of the PoA bounds for three classical games – weighted affine congestion games, competitive facility location games and simultaneous second price auctions. Our price anarchy bounds for these games match the ones known in the literature or obtained using the smoothness framework. All our proofs use the following technique: we first show that for a wide class of games, one can formulate the underlying optimization problem as a linear (or convex) program such that the (Fenchel) dual of the relaxation encodes the equilibrium condition. Further, the dual program has a specific structure with variables for players and resources, which can be naturally interpreted as the cost incurred by the players and the congestion of the resource in an equilibrium outcome. This lets us argue that our definition of dual variables satisfy the dual constraints and using the weak duality theorem we establish the PoA bounds. View details
    Preview abstract Constraints on agent's ability to pay play a major role in auction design for any setting where the magnitude of financial transactions is sufficiently large. Those constraints have been traditionally modeled in mechanism design as hard budget, i.e., mechanism is not allowed to charge agents more than a certain amount. Yet, real auction systems (such as Google AdWords) allow more sophisticated constraints on agents' ability to pay, such as average budgets. In this work, we investigate the design of Pareto optimal and incentive compatible auctions for agents with constrained quasi-linear utilities, which captures more realistic models of liquidity constraints that the agents may have. Our result applies to a very general class of allocation constraints known as polymatroidal environments, encompassing many settings of interest such as multi-unit auctions, matching markets, video-on demand and advertisement systems. Our design is based Ausubel's clinching framework. Incentive compatibility and feasibility with respect to ability-to-pay constraints are direct consequences of the clinching framework. Pareto-optimality, on the other hand, is considerably more challenging, since the no-trade condition that characterizes it depends not only on whether agents have their budgets exhausted or not, but also on prices {at} which the goods are allocated. In order to get a handle on those prices, we introduce novel concepts of dropping prices and saturation. These concepts lead to our main structural result which is a characterization of the tight sets in the clinching auction outcome and its relation to dropping prices. View details
    Preview abstract In this paper we consider efficient construction of “composable core-sets” for basic diversity and coverage maximization problems. A core-set for a point-set in a metric space is a subset of the point-set with the property that an approximate solution to the whole point-set can be obtained given the core-set alone. A composable core-set has the property that for a collection of sets, the approximate solution to the union of the sets in the collection can be obtained given the union of the composable core-sets for the point sets in the collection. Using composable core-sets one can obtain effi- cient solutions to a wide variety of massive data processing applications, including nearest neighbor search, streaming algorithms and map-reduce computation. Our main results are algorithms for constructing composable core-sets for several notions of “diversity objective functions”, a topic that attracted a significant amount of research over the last few years. The composable core-sets we construct are small and accurate: their approximation factor almost matches that of the best “off-line” algorithms for the relevant optimization problems (up to a constant factor). Moreover, we also show applications of our results to diverse nearest neighbor search, streaming algorithms and map-reduce computation. Finally, we show that for an alternative notion of diversity maximization based on the maximum coverage problem small composable core-sets do not exist. View details
    Distributed Balanced Clustering via Mapping Coresets
    Aditya Bhaskara
    NIPS, Neural Information Processing Systems Foundation (2014)
    Preview abstract Large-scale clustering of data points in metric spaces is an important problem in mining big data sets. For many applications, we face explicit or implicit size constraints for each cluster which leads to the problem of clustering under capacity constraints or the balanced clustering'' problem. Although the balanced clustering problem has been widely studied, developing a theoretically sound distributed algorithm remains an open problem. In the present paper we develop a general framework based on mapping coresets'' to tackle this issue. For a wide range of clustering objective functions such as k-center, k-median, and k-means, our techniques give distributed algorithms for balanced clustering that match the best known single machine approximation ratios. View details
    Preview abstract Computing connected components of a graph lies at the core of many data mining algorithms, and is a fundamental subroutine in graph clustering. This problem is well studied, yet many of the algorithms with good theoretical guarantees perform poorly in practice, especially when faced with graphs with hundreds of billions of edges. In this paper, we design improved algorithms based on traditional MapReduce architecture for large scale data analysis. We also explore the effect of augmenting MapReduce with a distributed hash table (DHT) service. We show that these algorithms have provable theoretical guarantees, and easily outperform previously studied algorithms, sometimes by more than an order of magnitude. In particular, our iterative MapReduce algorithms run 3 to 15 times faster than the best previously studied algorithms, and the MapReduce implementation using a DHT is 10 to 30 times faster than the best previously studied algorithms. These are the fastest algorithms that easily scale to graphs with hundreds of billions of edges. View details
    Multiplicative Bidding in Online Advertising
    Sam Chiu-wai Wong
    ACM Conference on Economics and Computation (EC) (2014)
    Preview abstract In this paper, we initiate the study of the multiplicative bidding language adopted by major Internet search companies. In multiplicative bidding, the effective bid on a particular search auction is the product of a base bid and bid adjustments that are dependent on features of the search (for example, the geographic location of the user, or the platform on which the search is conducted). We consider the task faced by the advertiser when setting these bid adjustments, and establish a foundational optimization problem that captures the core difficulty of bidding under this language. We give matching algorithmic and approximation hardness results for this problem; these results are against an information-theoretic bound, and thus have implications on the power of the multiplicative bidding language itself. Inspired by empirical studies of search engine price data, we then codify the relevant restrictions of the problem, and give further algorithmic and hardness results. Our main technical contribution is an O(log n)-approximation for the case of multiplicative prices and monotone values. We also provide empirical validations of our problem restrictions, and test our algorithms on real data against natural benchmarks. Our experiments show that they perform favorably compare with the baseline. View details
    Partner tiering in display advertising
    Anand Bhalgat
    Hennadiy Leontyev
    Max Lin
    WSDM (2014), pp. 133-142
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    Preview abstract A major challenge faced by the marketers attempting to optimize their advertising campaigns is to deal with budget constraints. The problem is even harder in the face of multidimensional budget constraints, particularly in the presence of many decision variables involved, and the interplay among the decision variables through these such constraints. Concise bidding strategies help advertisers deal with this challenge by introducing fewer variables to act on. In this paper, we study the problem of finding optimal concise bidding strategies for advertising campaigns with multiple budget constraints. Given bid landscapes—i.e., predicted value (e.g., number of clicks) and cost per click for any bid—that are typically provided by ad-serving systems, we optimize the value given budget constraints. In particular, we consider bidding strategies that consist of no more than k different bids for all keywords. For constant k, we provide a PTAS to optimize the profit, whereas for arbitrary k we show how constant-factor approximation can be obtained via a combination of solution enumeration and dependent LP-rounding techniques. Finally, we evaluate the performance of our algorithms on real datasets in two regimes with 1- and 3-dimensional budget constraint. In the former case where uniform bidding has provable performance guarantee, our algorithm beats the state of the art by an increase of 1% to 6% in the expected number of clicks. This is achieved by only two or three clusters—contrast with the single cluster permitted in uniform bidding. With only three dimensions in the budget constraint (one for total consumption, and another two for enforcing minimal diversity), the gap between the performance of our algorithm and an enhanced version of uniform bidding grows to an average of 5% to 6% (sometimes as high as 9%). Although the details of experiments for the multidimensional budget constraint to the full version of the paper are deferred to the full version of the paper, we report some highlights from the results. View details
    Coordination Mechanisms for Selfish Routing over Time on a Tree
    Sayan Bhattacharya
    Janardhan Kulkarni
    ICALP (1) (2014), pp. 186-197
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    Preview abstract We study the problem of computing similarity rankings in large-scale multi-categorical bipartite graphs, where the two sides of the graph represent actors and items, and the items are partitioned into an arbitrary set of categories. The problem has several real-world applications, including identifying competing advertisers and suggesting related queries in an online advertising system or finding users with similar interests and suggesting content to them. In these settings, we are interested in computing on-the-fly rankings of similar actors, given an actor and an arbitrary subset of categories of interest. Two main challenges arise: First, the bipartite graphs are huge and often lopsided (e.g. the system might receive billions of queries while presenting only millions of advertisers). Second, the sheer number of possible combinations of categories prevents the pre-computation of the results for all of them. We present a novel algorithmic framework that addresses both issues for the computation of several graph-theoretical similarity measures, including # common neighbors, and Personalized PageRank. We show how to tackle the imbalance in the graphs to speed up the computation and provide efficient real-time algorithms for computing rankings for an arbitrary subset of categories. Finally, we show experimentally the accuracy of our approach with real-world data, using both public graphs and a very large dataset from Google AdWords. View details
    Two-stage Robust Network Design with Exponential Scenarios
    Rohit Khandekar
    Guy Kortsarz
    Mohammad R. Salavatipour
    Algorithmica, vol. 65 (2013), pp. 391-408
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    Whole-page optimization and submodular welfare maximization with online bidders
    Nikhil Devanur
    Zhiyi Huang
    ACM Conference on Electronic Commerce (EC) 2013, pp. 305-322
    Preview abstract In the context of online ad serving, display ads may appear on different types of webpages, where each page includes several ad slots and therefore multiple ads can be shown on each page. The set of ads that can be assigned to ad slots of the same page needs to satisfy various prespecified constraints including exclusion constraints, diversity constraints, and the like. Upon arrival of a user, the ad serving system needs to allocate a set of ads to the current webpage respecting these per-page allocation constraints. Previous slot-based settings ignore the important concept of a page and may lead to highly suboptimal results in general. In this article, motivated by these applications in display advertising and inspired by the submodular welfare maximization problem with online bidders, we study a general class of page-based ad allocation problems, present the first (tight) constant-factor approximation algorithms for these problems, and confirm the performance of our algorithms experimentally on real-world datasets. A key technical ingredient of our results is a novel primal-dual analysis for handling free disposal, which updates dual variables using a “level function” instead of a single level and unifies with previous analyses of related problems. This new analysis method allows us to handle arbitrarily complicated allocation constraints for each page. Our main result is an algorithm that achieves a 1 &minus frac 1 e &minus o(1)-competitive ratio. Moreover, our experiments on real-world datasets show significant improvements of our page-based algorithms compared to the slot-based algorithms. Finally, we observe that our problem is closely related to the submodular welfare maximization (SWM) problem. In particular, we introduce a variant of the SWM problem with online bidders and show how to solve this problem using our algorithm for whole-page optimization. View details
    A Local Algorithm for Finding Well-Connected Clusters
    Zeyuan Allen Zhu
    The 30th International Conference on Machine Learning, ICML 2013
    Preview abstract Motivated by applications of large-scale graph clustering, we study random-walk-based LOCAL algorithms whose running times depend only on the size of the output cluster, rather than the entire graph. In particular, we develop a method with better theoretical guarantee compared to all previous work, both in terms of the clustering accuracy and the conductance of the output set. We also prove that our analysis is tight, and perform empirical evaluation to support our theory on both synthetic and real data. More specifically, our method outperforms prior work when the cluster is WELL-CONNECTED. In fact, the better it is well-connected inside, the more significant improvement we can obtain. Our results shed light on why in practice some random-walk-based algorithms perform better than its previous theory, and help guide future research about local clustering. View details
    Equilibrium pricing with positive externalities
    Nima AhmadiPourAnari
    Shayan Ehsani
    Mohammad Ghodsi
    Nima Haghpanah
    Nicole Immorlica
    Hamid Mahini
    Theor. Comput. Sci., vol. 476 (2013), pp. 1-15
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    PASS Approximation: A Framework for Analyzing and Designing Heuristics
    Uriel Feige
    Nicole Immorlica
    Hamid Nazerzadeh
    Algorithmica, vol. 66 (2013), pp. 450-478
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    Diversity maximization under matroid constraints
    Zeinab Abbassi
    Mayur Thakur
    KDD, ACM SIGKDD (2013), pp. 32-40
    Preview abstract Aggregator websites typically present documents in the form of representative clusters. In order for users to get a broader perspective, it is important to deliver a diversified set of representative documents in those clusters. One approach to diversification is to maximize the average dissimilarity among documents. Another way to capture diversity is to avoid showing several documents from the same category (e.g. from the same news channel). We combine the above two diversification concepts by modeling the latter approach as a (partition) matroid constraint, and study diversity maximization problems under matroid constraints. We present the first constant-factor approximation algorithm for this problem, using a new technique. Our local search 0:5-approximation algorithm is also the first constant-factor approximation for the max-dispersion problem under matroid constraints. Our combinatorial proof technique for maximizing diversity under matroid constraints uses the existence of a family of Latin squares which may also be of independent interest. In order to apply these diversity maximization algorithms in the context of aggregator websites and as a preprocessing step for our diversity maximization tool, we develop greedy clustering algorithms that maximize weighted coverage of a predefined set of topics. Our algorithms are based on computing a set of cluster centers, where clusters are formed around them. We show the better performance of our algorithms for diversity and coverage maximization by running experiments on real (Twitter) and synthetic data in the context of real-time search over micro-posts. Finally we perform a user study validating our algorithms and diversity metrics. View details
    Preview abstract Inspired by online ad allocation problems, many results have been developed for online matching problems. Most of the previous work deals with a single objective, but, in practice, there is a need to optimize multiple objectives. Here, as an illustrative example motivated by display ads allocation, we study a bi-objective online matching problem. In particular, we consider a set of fixed nodes (ads) with capacity constraints, and a set of online items (pageviews) arriving one by one. Upon arrival of an online item $i$, a set of eligible fixed neighbors (ads) for the item is revealed, together with a weight $w_{ia}$ for eligible neighbor $a$. The problem is to assign each item to an eligible neighbor online, while respecting the capacity constraints; the goal is to maximize both the total weight of the matching and the cardinality. In this paper, we present both approximation algorithms and hardness results for this problem. An $(\alpha, \beta)$-approximation for this problem is a matching with weight at least $\alpha$ fraction of the maximum weighted matching, and cardinality at least $\beta$ fraction of maximum cardinality matching. We present a parametrized approximation algorithm that allows a smooth tradeoff curve between the two objectives: when the capacities of fixed nodes are large, we give a $p(1- 1/e^{1/p}), (1-p)(1-1/e^{1/1-p})$-approximation for any $0 \le p \le 1$, and prove a `hardness curve' combining several inapproximability results. These upper and lower bounds are always close (with a maximum gap of $9\%$), and exactly coincide at the point $(0.43, 0.43)$. For small capacities, we present a smooth parametrized approximation curve for the problem between $(0,1-1/e)$ and $(1/2,0)$ passing through a $(1/3,0.3698)$-approximation. View details
    Preview abstract Auctions for perishable goods such as internet ad inventory need to make real-time allocation and pricing decisions as the supply of the good arrives in an online manner, without knowing the entire supply in advance. These allocation and pricing decisions get complicated when buyers have some global constraints. In this work, we consider a multi-unit model where buyers have global {\em budget} constraints, and the supply arrives in an online manner. Our main contribution is to show that for this setting there is an individually-rational, incentive-compatible and Pareto-optimal auction that allocates these units and calculates prices on the fly, without knowledge of the total supply. We do so by showing that the Adaptive Clinching Auction satisfies a {\em supply-monotonicity} property. We also analyze and discuss, using examples, how the insights gained by the allocation and payment rule can be applied to design better ad allocation heuristics in practice. Finally, while our main technical result concerns multi-unit supply, we propose a formal model of online supply that captures scenarios beyond multi-unit supply and has applications to sponsored search. We conjecture that our results for multi-unit auctions can be extended to these more general models. View details
    PASS Approximation: A Framework for Analyzing and Designing Heuristics.
    Uri Feige
    Nicole Immorlica
    Hamid Nazerzadeh
    Algorithmica, vol. 450-478 (2013)
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    On the advantage of overlapping clusters for minimizing conductance
    Rohit Khandekar
    Guy Kortsarz
    Proceedings of the 10th Latin American international conference on Theoretical Informatics, Springer-Verlag, Berlin, Heidelberg (2012), pp. 494-505
    Preview
    Preview abstract A central issue in applying auction theory in practice is the problem of dealing with budget-constrained agents. A desirable goal in practice is to design incentive compatible, individually rational, and Pareto optimal auctions while respecting the budget constraints. Achieving this goal is particularly challenging in the presence of nontrivial combinatorial constraints over the set of feasible allocations. Toward this goal and motivated by AdWords auctions, we present an auction for polymatroidal environments satisfying these properties. Our auction employs a novel clinching technique with a clean geometric description and only needs an oracle access to the submodular function defining the polymatroid. As a result, this auction not only simplifies and generalizes all previous results, it applies to several new applications including AdWords Auctions, bandwidth markets, and video on demand. In particular, our characterization of the AdWords auction as polymatroidal constraints might be of independent interest. This allows us to design the first mechanism for Ad Auctions taking into account simultaneously budgets, multiple keywords and multiple slots. We show that it is impossible to extend this result to generic polyhedral constraints. This also implies an impossibility result for multiunit auctions with decreasing marginal utilities in the presence of budget constraints. View details
    Convergence and approximation in potential games
    George Christodoulou
    Anastasios Sidiropoulos
    Theor. Comput. Sci., vol. 438 (2012), pp. 13-27
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    Overlapping clusters for distributed computation
    Reid Andersen
    David Gleich
    ACM Conference on Web Search and Data Mining (WSDM) (2012)
    Preview
    Preview abstract Motivated by online ad allocation, we study the problem of simultaneous approximations for the adversarial and stochastic online budgeted allocation problem. This problem consists of a bipartite graph G = (X, Y, E), where the nodes of Y along with their corresponding capacities are known beforehand to the algorithm, and the nodes of X arrive online. When a node of X arrives, its incident edges, and their respective weights are revealed, and the algorithm can match it to a neighbor in Y. The objective is to maximize the weight of the final matching, while respecting the capacities. When nodes arrive in an adversarial order, the best competitive ratio is known to be 1 - 1/e, and it can be achieved by the Ranking [18], and its generalizations (Balance [16, 21]). On the other hand, if the nodes arrive through a random permutation, it is possible to achieve a competitive ratio of 1 -- ε [9]. In this paper we design algorithms that achieve a competitive ratio better than 1 -- 1/e on average, while preserving a nearly optimal worst case competitive ratio. Ideally, we want to achieve the best of both worlds, i.e, to design an algorithm with the optimal competitive ratio in both the adversarial and random arrival models. We achieve this for unweighted graphs, but show that it is not possible for weighted graphs. In particular, for unweighted graphs, under some mild assumptions, we show that Balance achieves a competitive ratio of 1 -- ε in a random permutation model. For weighted graphs, however, we prove this is not possible; we prove that no online algorithm that achieves an approximation factor of 1 -- 1/ε for the worst-case inputs may achieve an average approximation factor better than 97.6% for random inputs. In light of this hardness result, we aim to design algorithms with improved approximation ratios in the random arrival model while preserving the competitive ratio of 1 -- 1/ε in the worst case. To this end, we show the algorithm proposed by [21] achieves a competitive ratio of 0.76 for the random arrival model, while having a 1 -- 1/ε ratio in the worst case. View details
    How to approximate optimal auctions
    Nima Haghpanah
    Nicole Immorlica
    Kamesh Munagala
    SIGecom Exchanges, vol. 11 (2012), pp. 30-33
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    Preview abstract While it is relatively easy to start an online advertising campaign, proper allocation of the marketing budget is far from trivial. A major challenge faced by the marketers attempting to optimize their campaigns is in the sheer number of variables involved, the many individual decisions they make in fixing or changing these variables, and the nontrivial short and long-term interplay among these variables and decisions. In this paper, we study interactions among individual advertising decisions using a Markov model of user behavior. We formulate the budget allocation task of an advertiser as a constrained optimal control problem for a Markov Decision Process (MDP). Using the theory of constrained MDPs, a simple LP algorithm yields the optimal solution. Our main result is that, under a reasonable assumption that online advertising has positive carryover effects on the propensity and the form of user interactions with the same advertiser in the future, there is a simple greedy algorithm for the budget allocation with the worst-case running time cubic in the number of model states (potential advertising keywords) and an efficient parallel implementation in a distributed computing framework like MapReduce. Using real-world anonymized datasets from sponsored search advertising campaigns of several advertisers, we evaluate performance of the proposed budget allocation algorithm, and show that the greedy algorithm performs well compared to the optimal LP solution on these datasets and that both show consistent 5-10% improvement in the expected revenue against the optimal baseline algorithm ignoring carryover effects. View details
    On the Non-progressive Spread of Influence through Social Networks
    MohammadAmin Fazli
    Mohammad Ghodsi
    Jafar Habibi
    Pooya Jalaly Khalilabad
    Sina Sadeghian
    LATIN (2012)
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    Preview abstract In light of the growing market of Ad Exchanges for the real-time sale of advertising slots, publishers face new challenges in choosing between the allocation of contract-based reservation ads and spot market ads. In this setting, the publisher should take into account the tradeoff between short-term revenue from an Ad Exchange and quality of allocating reservation ads. In this paper, we formalize this combined optimization problem as a stochastic control problem and derive an efficient policy for online ad allocation in settings with general joint distribution over placement quality and exchange bids. We prove asymptotic optimality of this policy in terms of any trade-off between quality of delivered reservation ads and revenue from the exchange, and provide a rigorous bound for its convergence rate to the optimal policy. We also give experimental results on data derived from real publisher inventory, showing that our policy can achieve any pareto-optimal point on the quality vs. revenue curve. Finally, we study a parametric training-based algorithm in which instead of learning the dual variables from a sample data (as is done in non-parametric training-based algorithms), we learn the parameters of the distribution and construct those dual variables from the learned parameter values. We compare parametric and non-parametric ways to estimate from data both analytically and experimentally in the special case without the ad exchange, and show that though both methods converge to the optimal policy as the sample size grows, our parametric method converges faster, and thus performs better on smaller samples. View details
    Inner Product Spaces for MinSum Coordination Mechanisms
    Richard Cole
    Jose R. Correa
    Vasilis Gkatzelis
    Neil Olver
    STOC (2011)
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    Optimal Auctions with Positive Network Externalities
    Nima Haghpanah
    Nicole Immorlica
    K. Munagala
    ACM Conference on Electronic Commerce (2011)
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    Equilibrium Pricing with Positive Externalities (Extended Abstract)
    Nima Anari
    Shayan Ehsani
    Mohammad Ghodsi
    Nima Haghpanah
    Nicole Immorlica
    Hamid Mahini
    WINE (2010), pp. 424-431
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    Optimal Iterative Pricing over Social Networks (Extended Abstract)
    Hessameddin Akhlaghpour
    Mohammad Ghodsi
    Nima Haghpanah
    Hamid Mahini
    Afshin Nikzad
    WINE (2010), pp. 415-423
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    Auctions with intermediaries: extended abstract
    S. Muthukrishnan
    Mallesh M. Pai
    ACM Conference on Electronic Commerce (2010), pp. 23-32
    Preview abstract Inspired by online advertisement exchange systems, we study a setting where potential buyers of a unique, indivisible good attempt to purchase from a central seller via a set of intermediaries. Each intermediary has captive buyers, and runs an auction for a 'contingent' good. Based on the outcome, the intermediary bids in a subsequent upstream auction run by the seller. In this paper, we study the equilibria and incentives of intermediaries and the central seller. We find that combining the notion of optimal auction design with the double-marginalization arising from the presence of intermediaries yields new strategic elements not present in either setting individually: we show that in equilibrium, revenue-maximizing intermediaries will use an auction with a randomized reserve price chosen from an interval. We characterize the interval and the probability distribution from which this reserve price is chosen as a function of the distribution of buyers' types. Furthermore, we characterize the revenue maximizing auction for the central seller by taking into account the effect of his choice of mechanism on the mechanisms offered by the intermediaries. We find that the optimal reserve price offered by the seller decreases with the number of buyers (but remains strictly positive); in contrast to the classical optimal auction without intermediaries, where the reserve price is independent of the number of buyers. View details
    Preview abstract Inspired by online ad allocation, we study online stochastic packing integer programs from theoretical and practical standpoints. We first present a near-optimal online algorithm for a general class of packing integer programs which model various online resource allocation problems including online variants of routing, ad allocations, generalized assignment, and combinatorial auctions. As our main theoretical result, we prove that a simple dual training-based algorithm achieves a (1 − o(1))-approximation guarantee in the random order stochastic model. This is a significant improvement over logarithmic or constant-factor approximations for the adversarial variants of the same problems (e.g. factor 1−1e1−1e for online ad allocation, and log(m) for online routing). We then focus on the online display ad allocation problem and study the efficiency and fairness of various training-based and online allocation algorithms on data sets collected from real-life display ad allocation system. Our experimental evaluation confirms the effectiveness of training-based algorithms on real data sets, and also indicates an intrinsic trade-off between fairness and efficiency. View details
    Maximizing Nonmonotone Submodular Functions under Matroid or Knapsack Constraints
    Jon Lee
    Viswanath Nagarajan
    Maxim Sviridenko
    SIAM J. Discrete Math., vol. 23 (2010), pp. 2053-2078
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    On the complexity of nash dynamics and sink equilibria
    Alexander Skopalik
    ACM Conference on Electronic Commerce (2009), pp. 1-10
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    Bid optimization for broad match ad auctions
    Eyal Even-Dar
    S. Muthukrishnan
    Yishay Mansour
    WWW (2009), pp. 231-240
    Preview
    Online Stochastic Matching: Beating 1-1/e
    S. Muthukrishnan
    Symposium on the Foundations of Computer Science (FOCS) (2009)
    Preview abstract We study the online stochastic bipartite matching problem, in a form motivated by display ad allocation on the Internet. In the online, but adversarial case, the celebrated result of Karp, Vazirani and Vazirani gives an approximation ratio of 1−1e≃0.632, a very familiar bound that holds for many online problems; further, the bound is tight in this case. In the online, stochastic case when nodes are drawn repeatedly from a known distribution, the greedy algorithm matches this approximation ratio, but still, no algorithm is known that beats the 1−1e bound.Our main result is a 0.67-approximation online algorithm for stochastic bipartite matching, breaking this 1−1e barrier. Furthermore, we show that no online algorithm can produce a 1−ϵ approximation for an arbitrarily small ϵ for this problem. Our algorithms are based on computing an optimal offline solution to the expected instance, and using this solution as a guideline in the process of online allocation. We employ a novel application of the idea of the power of two choices from load balancing: we compute two disjoint solutions to the expected instance, and use both of them in the online algorithm in a prescribed preference order. To identify these two disjoint solutions, we solve a max flow problem in a boosted flow graph, and then carefully decompose this maximum flow to two edge-disjoint (near-) matchings. In addition to guiding the online decision making, these two offline solutions are used to characterize an upper bound for the optimum in any scenario. This is done by identifying a cut whose value we can bound under the arrival distribution. At the end, we discuss extensions of our results to more general bipartite allocations that are important in a display ad application. View details
    Coordination mechanisms for selfish scheduling
    Nicole Immorlica
    Li (Erran) Li
    Andreas S. Schulz
    Theor. Comput. Sci., vol. 410 (2009), pp. 1589-1598
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    PASS Approximation
    Uriel Feige
    Nicole Immorlica
    Hamid Nazerzadeh
    APPROX-RANDOM (2009), pp. 111-124
    Preview
    Non-monotone submodular maximization under matroid and knapsack
    Jon Lee
    Viswanath Nagarajan
    Maxim Sviridenko
    STOC (2009), pp. 323-332
    Preview
    Approximating Submodular Functions Everywhere
    Michel Goemans
    Nick Harvey
    S. Iwata
    Symposium on Discrete Algorithms (SODA) (2009)
    Preview
    Competitive Routing over Time
    Martin Hoefer
    Heiko Röglin
    Shang-Hua Teng
    Workshop of Internet Economics (WINE) (2009), pp. 18-29
    Preview
    Permutation betting markets: singleton betting with extra information
    Mohammad Ghodsi
    Hamid Mahini
    ACM Conference on Electronic Commerce (2008), pp. 180-189
    Preview
    Two-Stage Robust Network Design with Exponential Scenarios
    Rohit Khandekar
    Guy Kortsarz
    Mohammad R. Salavatipour
    ESA (2008), pp. 589-600
    Preview
    On non-progressive spread of influence through social networks
    MohammadAmin Fazli
    Mohammad Ghodsi
    Jafar Habibi
    Pooya Jalaly Khalilabadi
    Sina Sadeghian Sadeghabad
    Theor. Comput. Sci., vol. 550 (2014), pp. 36-50
    Tight Approximation Algorithms for Maximum Separable Assignment Problems
    Lisa Fleischer
    Michel X. Goemans
    Maxim Sviridenko
    Math. Oper. Res., vol. 36 (2011), pp. 416-431
    Secure Overlay Network Design
    Li (Erran) Li
    Algorithmica, vol. 57 (2010), pp. 82-96
    Online Stochastic Ad Allocation: Efficiency and Fairness
    Monika Henzinger
    Clifford Stein
    CoRR, vol. abs/1001.5076 (2010)
    Coordination Mechanisms for Weighted Sum of Completion Times in Machine Scheduling
    Richard Cole 0001
    Vasilis Gkatzelis
    CoRR, vol. abs/1010.1886 (2010)
    Non-monotone submodular maximization under matroid and knapsack constraints
    Jon Lee
    Viswanath Nagarajan
    Maxim Sviridenko
    CoRR, vol. abs/0902.0353 (2009)
    Bid Optimization in Broad-Match Ad Auctions
    Eyal Even-Dar
    Yishay Mansour
    S. Muthukrishnan
    Uri Nadav
    CoRR, vol. abs/0901.3754 (2009)
    Non-monotone submodular maximization under matroid and knapsack constraints
    Jon Lee
    Viswanath Nagarajan
    Maxim Sviridenko
    STOC (2009), pp. 323-332
    (Almost) optimal coordination mechanisms for unrelated machine scheduling
    Yossi Azar
    Kamal Jain
    SODA (2008), pp. 323-332
    Approximating Minimum-Power Degree and Connectivity Problems
    Guy Kortsarz
    Zeev Nutov
    Elena Tsanko
    LATIN (2008), pp. 423-435
    On the Stability of Web Crawling and Web Search
    Reid Andersen
    Christian Borgs
    Jennifer T. Chayes
    John E. Hopcroft
    Shang-Hua Teng
    ISAAC (2008), pp. 680-691
    Tight information-theoretic lower bounds for welfare maximization in combinatorial auctions
    Michael Schapira
    Jan Vondrák
    ACM Conference on Electronic Commerce (2008), pp. 70-77
    Market Games and Content Distribution
    Encyclopedia of Algorithms (2008)
    The myth of the folk theorem
    Christian Borgs
    Jennifer T. Chayes
    Nicole Immorlica
    Adam Tauman Kalai
    Christos H. Papadimitriou
    STOC (2008), pp. 365-372
    Fast convergence to nearly optimal solutions in potential games
    Baruch Awerbuch
    Yossi Azar
    Amir Epstein
    Alexander Skopalik
    ACM Conference on Electronic Commerce (2008), pp. 264-273
    Optimal marketing strategies over social networks
    Jason D. Hartline
    WWW (2008), pp. 189-198
    A combinatorial allocation mechanism with penalties for banner advertising
    Uriel Feige
    Nicole Immorlica
    Hamid Nazerzadeh
    WWW (2008), pp. 169-178
    Limitations of cross-monotonic cost-sharing schemes
    Nicole Immorlica
    ACM Transactions on Algorithms, vol. 4 (2008)
    Robust PageRank and locally computable spam detection features
    Reid Andersen
    Christian Borgs
    Jennifer T. Chayes
    John E. Hopcroft
    Kamal Jain
    Shang-Hua Teng
    AIRWeb (2008), pp. 69-76
    Uncoordinated two-sided matching markets
    Heiner Ackermann
    Paul W. Goldberg
    Heiko R{\
    Berthold V{\
    ACM Conference on Electronic Commerce (2008), pp. 256-263
    Trust-based recommendation systems: an axiomatic approach
    Reid Andersen
    Christian Borgs
    Jennifer T. Chayes
    Uriel Feige
    Abraham D. Flaxman
    Adam Kalai
    Moshe Tennenholtz
    WWW (2008), pp. 199-208
    Robust Combinatorial Optimization with Exponential Scenarios
    Uriel Feige
    Kamal Jain
    IPCO (2007), pp. 439-453
    Power optimization in fault-tolerant topology control algorithms for wireless multi-hop networks
    Mohammad Taghi Hajiaghayi
    Nicole Immorlica
    IEEE/ACM Trans. Netw., vol. 15 (2007), pp. 1345-1358
    A Recommender System Based on Local Random Walks and Spectral Methods
    Zeinab Abbassi
    WebKDD/SNA-KDD (2007), pp. 139-153
    Subjective-cost policy routing
    Joan Feigenbaum
    David R. Karger
    Rahul Sami
    Theor. Comput. Sci., vol. 378 (2007), pp. 175-189
    Cell Breathing in Wireless LANs: Algorithms and Evaluation
    Paramvir Bahl
    Mohammad Taghi Hajiaghayi
    Kamal Jain
    Lili Qiu
    Amin Saberi
    IEEE Trans. Mob. Comput., vol. 6 (2007), pp. 164-178
    Maximizing Non-Monotone Submodular Functions
    Uriel Feige
    Jan Vondrák
    FOCS (2007), pp. 461-471
    Local Computation of PageRank Contributions
    Reid Andersen
    Christian Borgs
    Jennifer T. Chayes
    John E. Hopcraft
    Shang-Hua Teng
    WAW (2007), pp. 150-165
    A Unified Approach to Congestion Games and Two-Sided Markets
    Heiner Ackermann
    Paul W. Goldberg
    Heiko R{\
    Berthold V{\
    WINE (2007), pp. 30-41
    Market sharing games applied to content distribution in ad hoc networks
    Michel X. Goemans
    Li Li
    Marina Thottan
    IEEE Journal on Selected Areas in Communications, vol. 24 (2006), pp. 1020-1033
    Tight approximation algorithms for maximum general assignment problems
    Lisa Fleischer
    Michel X. Goemans
    Maxim Sviridenko
    SODA (2006), pp. 611-620
    Bandwidth Sharing Network Design for Multi-Class Traffic
    Mohammad Taghi Hajiaghayi
    Li Li
    Marina Thottan
    INFOCOM (2006)
    Assignment Problems in Rental Markets
    David Abraham
    Ning Chen
    Vijay Kumar
    WINE (2006), pp. 198-213
    A relation between choosability and uniquely list colorability
    Saieed Akbari
    Bashir S. Sadjad
    J. Comb. Theory, Ser. B, vol. 96 (2006), pp. 577-583
    Convergence and Approximation in Potential Games
    George Christodoulou
    Anastasios Sidiropoulos
    STACS (2006), pp. 349-360
    Secure Overlay Network Design
    Erran L. Li
    AAIM (2006), pp. 354-366
    Fault-Tolerant and 3-Dimensional Distributed Topology Control Algorithms in Wireless Multi-hop Networks
    Mohsen Bahramgiri
    Mohammad Taghi Hajiaghayi
    Wireless Networks, vol. 12 (2006), pp. 179-188
    Sink Equilibria and Convergence
    Michel X. Goemans
    Adrian Vetta
    FOCS (2005), pp. 142-154
    Limitations of cross-monotonic cost sharing schemes
    Nicole Immorlica
    SODA (2005), pp. 602-611
    Power Optimization for Connectivity Problems
    Mohammad Taghi Hajiaghayi
    Guy Kortsarz
    Zeev Nutov
    IPCO (2005), pp. 349-361
    Coordination Mechanisms for Selfish Scheduling
    Nicole Immorlica
    Li Li
    Andreas Schulz
    WINE (2005), pp. 55-69
    Cycle Cover with Short Cycles
    Nicole Immorlica
    STACS (2005), pp. 641-653
    Subjective-Cost Policy Routing
    Joan Feigenbaum
    David R. Karger
    Rahul Sami
    WINE (2005), pp. 174-183
    Traffic engineering of management flows by link augmentations on confluent trees
    Randeep Bhatia
    Nicole Immorlica
    Tracy Kimbrel
    Seffi Naor
    Baruch Schieber
    SPAA (2005), pp. 289-298
    Market sharing games applied to content distribution in ad-hoc networks
    Michel X. Goemans
    Erran L. Li
    Marina Thottan
    MobiHoc (2004), pp. 55-66
    Convergence Issues in Competitive Games
    Adrian Vetta
    APPROX-RANDOM (2004), pp. 183-194
    On spectrum sharing games
    Magnús M. Halldórsson
    Joseph Y. Halpern
    Erran L. Li
    PODC (2004), pp. 107-114
    Locality-sensitive hashing scheme based on p-stable distributions
    Mayur Datar
    Nicole Immorlica
    Piotr Indyk
    Symposium on Computational Geometry (2004), pp. 253-262
    A Simple Polynomial Time Framework For Reduced Path Decomposition in Multi-Path Routing
    Marina Thottan
    H{\
    Sanjoy Paul
    INFOCOM (2004)
    Distributed Network Monitoring for Evolving IP Networks
    Marina Thottan
    Erran L. Li
    Bin Yao
    Sanjoy Paul
    ICDCS (2004), pp. 712-719
    On the costs and benefits of procrastination: approximation algorithms for stochastic combinatorial optimization problems
    Nicole Immorlica
    David R. Karger
    Maria Minkoff
    SODA (2004), pp. 691-700
    Power optimization in fault-tolerant topology control algorithms for wireless multi-hop networks
    Mohammad Taghi Hajiaghayi
    Nicole Immorlica
    MOBICOM (2003), pp. 300-312
    The facility location problem with general cost functions
    Mohammad Taghi Hajiaghayi
    Networks, vol. 42 (2003), pp. 42-47
    RoboCup-2001: The Fifth Robotic Soccer World Championships
    Manuela M. Veloso
    Tucker R. Balch
    Peter Stone
    Hiroaki Kitano
    Fuminori Yamasaki
    Ken Endo
    Minoru Asada
    Mansour Jamzad
    Sayyed Bashir Sadjad
    Moslem Kazemi
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    Abbas Heydarnoori
    Mohammad Taghi Hajiaghayi
    Ehsan Chiniforooshan
    AI Magazine, vol. 23 (2002), pp. 55-68
    Length-constrained path-matchings in graphs
    Mohammad Ghodsi
    Mohammad Taghi Hajiaghayi
    Networks, vol. 39 (2002), pp. 210-215
    A Fast Vision System for Middle Size Robots in RoboCup
    Mansour Jamzad
    Sayyed Bashir Sadjad
    Moslem Kazemi
    Hamid Reza Chitsaz
    Abbas Heydarnoori
    Mohammad Taghi Hajiaghayi
    Ehsan Chiniforooshan
    RoboCup (2001), pp. 71-80
    K_r-Free Uniquely Vertex Colorable Graphs with Minimum Possible Edges
    Saeed Akbari
    Sayyed Bashir Sadjad
    J. Comb. Theory, Ser. B, vol. 82 (2001), pp. 316-318
    Basic Requirements for a Teamwork in Middle Size RoboCup
    Mansour Jamzad
    Hamid Reza Chitsaz
    Amirali Foroughnassiraei
    Reza Ghorbani
    Moslem Kazemi
    Sayyed Bashir Sadjad
    RoboCup (2001), pp. 621-626
    On the simultaneous edge-coloring conjecture
    Mohammad Taghi Hajiaghayi
    Ebadollah S. Mahmoodian
    Amin Saberi
    Ruzbeh Tusserkani
    Discrete Mathematics, vol. 216 (2000), pp. 267-272
    A Goal Keeper for Middle Size RoboCup
    Mansour Jamzad
    Amirali Foroughnassiraei
    Mohammad Taghi Hajiaghayi
    Reza Ghorbani
    Abbas Heydarnoori
    Moslem Kazemi
    Hamid Reza Chitsaz
    Farid Mobasser
    Mohsen Ebrahimi Moghaddam
    M. Gudarzi
    N. Ghaffarzadegan
    RoboCup (2000), pp. 583-586