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Ravi Kumar

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    Preview abstract We propose a new family of label randomization mechanisms for the task of training regression models under the constraint of label differential privacy (DP). In particular, we leverage the trade-offs between bias and variance to construct better noising mechanisms depending on a privately estimated prior distribution over the labels. We demonstrate that these mechanisms achieve state-of-the-art privacy-accuracy trade-offs on several datasets, highlighting the importance of bias-reducing constraints when training neural networks with label DP. We also provide theoretical results shedding light on the structural properties of the optimal bias-reduced mechanisms. View details
    Preview abstract We study the problem of releasing the weights of all-pairs shortest paths in a weighted undirected graph with differential privacy (DP). In this setting, the underlying graph is fixed and two graphs are neighbors if their edge weights differ by at most 1 in the ℓ1-distance. We give an algorithm with additive error ̃O(n^2/3/ε) in the ε-DP case and an algorithm with additive error ̃O(√n/ε) in the (ε, δ)-DP case, where n denotes the number of vertices. This positively answers a question of Sealfon [Sea16, Sea20], who asked whether a o(n) error algorithm exists. We also show that an additive error of Ω(n1/6) is necessary for any sufficiently small ε, δ > 0. Furthermore, we show that if the graph is promised to have reasonably bounded weights, one can improve the error further to roughly n^{(√17−3)/2+o(1)}/ε in the ε-DP case and roughly n^{√2−1+o(1)}/ε in the (ε, δ)-DP case. Previously, it was only known how to obtain ̃O(n2/3/ε1/3) additive error in the ε-DP case and ̃O(√n/ε) additive error in the (ε, δ)-DP case for bounded-weight graphs [Sea16]. Finally, we consider a relaxation where a multiplicative approximation is allowed. We show that, with a multiplicative approximation factor k, the additive error can be reduced to ̃O(n^{1/2+O(1/k)}/ε) in the ε-DP case and ̃O(n^{1/3+O(1/k)}/ε) in the (ε, δ)-DP case. View details
    Preview abstract Differential privacy is often applied with a privacy parameter that is larger than the theory suggests is ideal; various informal justifications for tolerating large privacy parameters have been proposed. In this work, we consider partial differential privacy (DP), which allows quantifying the privacy guarantee on a per-attribute basis. In this framework, we study several basic data analysis and learning tasks, and design algorithms whose per-attribute privacy parameter is smaller that the best possible privacy parameter for the entire record of a person (i.e., all the attributes). View details
    Preview abstract In this work, we study the task of estimating the numbers of distinct and k-occurring items in a time window under the constraint of differential privacy (DP). We consider several variants depending on whether the queries are on general time windows (between times t1 and t2), or are restricted to being cumulative (between times 1 and t2), and depending on whether the DP neighboring relation is event-level or the more stringent item-level. We obtain nearly tight upper and lower bounds on the errors of DP algorithms for these problems. En route, we obtain an event-level DP algorithm for estimating, at each time step, the number of distinct items seen over the last W updates with error polylogarithmic in W; this answers an open question of Bolot et al. (ICDT 2013). View details
    Preview abstract In this work, we study the large-scale pretraining of BERT-Large~\citep{devlin2018bert} with differentially private SGD (DP-SGD). We show that combined with a careful implementation, scaling up the batch size to millions (i.e., mega-batches) improves the utility of the DP-SGD step for BERT; we also enhance the training efficiency by using an increasing batch size schedule. Our implementation builds on the recent work of \citet{subramani20}, who demonstrated that the overhead of a DP-SGD step is minimized with effective use of JAX \cite{jax2018github, frostig2018compiling} primitives in conjunction with the XLA compiler \cite{xladocs}. Our implementation achieves a masked language model accuracy of 60.5\% at a batch size of 2M, for $\eps = 5$, which is a reasonable privacy setting. To put this number in perspective, non-private BERT models achieve an accuracy of $\sim$70\%. View details
    Preview abstract We consider the computation of sparse, (ε, ϑ)-differentially private~(DP) histograms in the two-server model of secure multi-party computation~(MPC), which has recently gained traction in the context of privacy-preserving measurements of aggregate user data. We introduce protocols that enable two semi-honest non-colluding servers to compute histograms over the data held by multiple users, while only learning a private view of the data. Our solution achieves the same asymptotic l∞-error of O(log(1/ϑ)/ε) as in the central model of DP, but without relying on a trusted curator. The server communication and computation costs of our protocol are independent of the number of histogram buckets, and are linear in the number of users, while the client cost is independent of the number of users, ε, and ϑ. Its linear dependence on the number of users lets our protocol scale well, which we confirm using microbenchmarks: for a billion users, ε = 0.5, and ϑ = 10-11, the per-user cost of our protocol is only 1.08 ms of server computation and 339 bytes of communication. In contrast, a baseline protocol using garbled circuits only allows up to 106 users, where it requires 600 KB communication per user. View details
    Preview abstract In this paper, we consider the problem of differentially private (DP) algorithms for isotonic regression. For the most general problem of isotonic regression over a partially ordered set (poset) X and for any Lipschitz loss function, we obtain a pure-DP algorithm that, given n input points, has an expected excess empirical risk of roughly width(X)⋅log|X|/n, where width(X) is the width of the poset. In contrast, we also obtain a near-matching lower bound of roughly (width(X)+log|X|)/n, that holds even for approximate-DP algorithms. Moreover, we show that the above bounds are essentially the best that can be obtained without utilizing any further structure of the poset. In the special case of a totally ordered set and for ℓ1 and ℓ2^2 losses, our algorithm can be implemented in near-linear running time; we also provide extensions of this algorithm to the problem of private isotonic regression with additional structural constraints on the output function. View details
    Preview abstract We introduce a new algorithm for numerical composition of privacy random variables, useful for computing the accurate privacy parameters for compositions of mechanisms. For the task of self-composing a broad class of mechanisms $K$ times, this algorithm achieves a running time \& memory usage of $\polylog(K)$ (e.g., this class includes the sub-sampled Gaussian mechanism, that appears in the analysis of DP-SGD). By comparison, recent work by Gopi et al. (NeurIPS 2021) has a running time of $\wtilde{O}(\sqrt{K})$ for the same task. Our approach extends to the case of composing $K$ different mechanisms in the same class, improving upon the running time / memory usage in the work of Gopi et al. from $\wtilde{O}(K^{1.5})$ to $\wtilde{O}(K)$. View details
    Preview abstract In this paper we consider the problem of aggregating multiple user-generated tracks in a differentially private manner. For this problem we propose a new aggregation algorithm that adds noise sufficient enough to guarantee privacy while preserving the utility of the aggregate. Under natural and simple assumptions, we also show that this algorithm has provably good guarantees. View details
    Preview abstract The privacy loss distribution (PLD) provides a tight characterization of the privacy loss of a mechanism in the context of differential privacy (DP). Recent work has shown that PLD-based accounting allows for tighter (ε,δ)-DP guarantees for many popular mechanisms compared to other known methods. A key question in PLD-based accounting is how to approximate any (potentially continuous) PLD with a PLD over any specified discrete support. We present a novel approach to this problem. Our approach supports both pessimistic estimation, which overestimates the hockey-stick divergence (i.e., δ) for any value of ε, and optimistic estimation, which underestimates the hockey-stick divergence. Moreover, we show that our pessimistic estimate is the best possible among all pessimistic estimates. Experimental evaluation shows that our approach can work with much larger discretization intervals while keeping a similar error bound compared to previous approaches and yet give a better approximation than existing methods. View details
    The Gibbs--Rand Model
    Flavio Chierichetti
    PODS 2022 (to appear)
    Preview abstract Thanks to its many applications the clustering ensemble problem has been extensively studied in the past. In htis problem we are giving in input $m$ clustering and the objective is to output a clustering that ``well-represent'' all the input clustering. In this paper, we propose to thee best of our knowledge the first generative model for the problem. Our model is parameterized by a ``center'' clustering and a scale; the probability of a particular clustering is an exponential function of its Rand distance to the center, scaled. For this new model, we show: (i) a sampling algorithm that runs in polynomial time when the center has a constant number of clusters and (ii) a simple polynomial time reconstruction algorithm when the scale is small. View details
    Preview abstract In social choice theory, (Kemeny) rank aggregation is a well-studied problem where the goal is to combine rankings from multiple voters into a single ranking on the same set of items. Since rankings can reveal preferences of voters (which a voter might like to keep private), it is important to aggregate preferences in such a way to preserve privacy. In this work, we present differentially private algorithms for rank aggregation in the pure and approximate settings along with distribution-independent utility upper and lower bounds. In addition to bounds in the central model, we also present utility bounds for the local model of differential privacy. View details
    Preview abstract We study the problem of privately computing the \emph{anonymized histogram} (aka \emph{unattributed histogram}), which is defined as the histogram without item labels. Previous works have provided algorithms with $\ell_1$ and $\ell_2$ errors of $O_\eps(\sqrt{n})$ in the central model of differential privacy (DP). In this work, we provide an algorithm with a nearly matching error guarantee of $\tilde{O}_\eps(\sqrt{n})$ in the shuffle and pan private DP models. Our algorithm is very simple: it just post-processes the discrete Laplace-noised histogram! Using this algorithm as a subroutine, we show applications in estimating several symmetric properties of distributions such as the entropy and support size. View details
    Preview abstract In this paper we prove that the sample complexity of properly learning a class of Littlestone dimension d with approximate differential privacy is Õ(d^6), ignoring privacy and accuracy parameters. This result answers a question of Bun et al. (FOCS 2020) by improving upon their upper bound of 2^O(d) on the sample complexity. Prior to our work, finiteness of the sample complexity for privately learning a class of finite Littlestone dimension was only known for improper private learners, and the fact that our learner is proper answers another question of Bun et al., which was also asked by Bousquet et al. (NeurIPS 2020). Using machinery developed by Bousquet et al., we then show that the sample complexity of sanitizing a binary hypothesis class is at most polynomial in its Littlestone dimension and dual Littlestone dimension. This implies that a class is sanitizable if and only if it has finite Littlestone dimension. An important ingredient of our proofs is a new property of binary hypothesis classes that we call irreducibility, which may be of independent interest. View details
    Preview abstract An exciting new development in differential privacy is the shuffled model, in which an anonymous channel enables non-interactive, differentially private protocols with error much smaller than what is possible in the local model, while relying on weaker trust assumptions than in the central model. In this paper, we study basic counting problems in the shuffled model and establish separations between the error that can be achieved in the single-message shuffled model and in the shuffled model with multiple messages per user. For the problem of frequency estimation for n users and a domain of size B, we obtain: - A nearly tight lower bound of Ω~(min(n^(1/4), B^(1/2))) on the error in the single-message shuffled model. This implies that the protocols obtained from the amplification via shuffling work of Erlingsson et al. (SODA 2019) and Balle et al. (Crypto 2019) are essentially optimal for single-message protocols. A key ingredient in the proof is a lower bound on the error of locally-private frequency estimation in the low-privacy (aka high ϵ) regime. - Protocols in the multi-message shuffled model with poly(log B, log n) bits of communication per user and polylog(B) error, which provide an exponential improvement on the error compared to what is possible with single-message algorithms. For the related selection problem on a domain of size B, we prove: - A nearly tight lower bound of Ω(B) on the number of users in the single-message shuffled model. This significantly improves on the Ω(B^{1/17}) lower bound obtained by Cheu et al. (Eurocrypt 2019), and when combined with their O~(B^{1/2})-error multi-message protocol, implies the first separation between single-message and multi-message protocols for this problem. View details
    Robust and Private Learning of Halfspaces
    Thao Nguyen
    International Conference on Artificial Intelligence and Statistics (AISTATS) (2021), pp. 1603-1611
    Preview abstract In this work, we study the trade-off between differential privacy and adversarial robustness under L2-perturbations in the context of learning halfspaces. We prove nearly tight bounds on the sample complexity of robust private learning of halfspaces for a large regime of parameters. A highlight of our results is that robust and private learning is harder than robust or private learning alone. We complement our theoretical analysis with experimental results on the MNIST and USPS datasets, for a learning algorithm that is both differentially private and adversarially robust. View details
    Google COVID-19 Vaccination Search Insights: Anonymization Process Description
    Adam Boulanger
    Akim Kumok
    Arti Patankar
    Benjamin Miller
    Chaitanya Kamath
    Charlotte Stanton
    Chris Scott
    Damien Desfontaines
    Evgeniy Gabrilovich
    Gregory A. Wellenius
    John S. Davis
    Karen Lee Smith
    Krishna Kumar Gadepalli
    Mark Young
    Shailesh Bavadekar
    Tague Griffith
    Yael Mayer
    Arxiv.org (2021)
    Preview abstract This report describes the aggregation and anonymization process applied to the COVID-19 Vaccination Search Insights~\cite{vaccination}, a publicly available dataset showing aggregated and anonymized trends in Google searches related to COVID-19 vaccination. The applied anonymization techniques protect every user’s daily search activity related to COVID-19 vaccinations with $(\varepsilon, \delta)$-differential privacy for $\varepsilon = 2.19$ and $\delta = 10^{-5}$. View details
    Locally Private k-Means in One Round
    Alisa Chang
    International Conference on Machine Learning (ICML) (2021), pp. 1441-1451
    Preview abstract We study k-means clustering in the non-interactive (aka one-round) local model of differential privacy. We give an approximation algorithm that requires a single round of communication and achieves an approximation ratio arbitrarily close to the best non private approximation algorithm. To show the flexibility of our framework, we also demonstrate that it yields a similar near-optimal approximation algorithm in the (one-round) shuffle model. View details
    Near-tight closure bounds for Littlestone and threshold dimensions
    Noah Golowich
    International Conference on Algorithmic Learning Theory (ALT) (2021), pp. 686-696
    Preview abstract We study closure properties for the Littlestone and threshold dimensions of binary hypothesis classes. Given classes H1,…,Hk of Boolean functions with bounded Littlestone (respectively, threshold) dimension, we establish an upper bound on the Littlestone (respectively, threshold) dimension of the class defined by applying an arbitrary binary aggregation rule to H1,…,Hk. We also show that our upper bounds are nearly tight. Our upper bounds give an exponential (in k) improvement upon analogous bounds shown by Alon et al. (COLT 2020), thus answering a question posed by their work. View details
    Preview abstract Most works in learning with differential privacy (DP) have focused on the case where each user has a single sample. In this work, we consider the setting where each user receives $m$ samples and the privacy protection is enforced at the level of each user's data. We show that, in this setting, we may learn with much few number of samples. Specifically, we show that, as long as each user receives sufficiently many samples, we can learn any privately learnable class via an $(\eps, \delta)$-DP algorithm using only $O(\log(1/\delta)/\eps)$ users. For $\eps$-DP algorithms, we show that we can learn using only $O_{\eps}(d)$ users even in the local model, where $d$ is the probabilistic representation dimension. In both cases, we show a nearly-matching lower bound on the number of users required. A crucial component of our results is a generalization of \emph{global stability}~\cite{BunLM20} that allows the use of public randomness. Under this relaxed notion, we employ a correlated sampling strategy to show that the global stability can be boosted to be arbitrarily close to one, at a polynomial expense in the number of samples. View details
    Preview abstract We study the setup where each of n users holds an element from a discrete set, and the goal is to count the number of distinct elements across all users, under the constraint of (epsilon, delta)-differentially privacy: - In the local setting, we prove that the additive error of any protocol is Omega(n) for any constant epsilon and any delta inverse polynomial in n. This provides the first separation between global sensitivity and error that is omega(sqrt{n}) in local differential privacy, thus answering a question of Vadhan (2017). - In the single-message shuffle setting, we prove a lower bound of tilde{Omega}(n) on the error for any constant epsilon and for some delta inverse quasi-polynomial in n. We do so using the moment-matching method from the literature on distribution estimation. - In the multi-message shuffle setting, we give a protocol with <= 1 message per user in expectation and with an error of tilde{O}(sqrt{n}) for any constant epsilon and delta inverse polynomial in n. Our proof technique relies on a new notion, that we call dominated protocols, and which can be used to obtain the first non-trivial lower bounds against multi-message shuffle protocols for the well-studied problems of Selection and Parity Learning. View details
    Preview abstract In this work, we study the problem of answering k queries with (ε, δ)-differential privacy, where each query has sensitivity one. We give a mechanism for this task that achieves an error bound of O(sqrt(k ln(1/δ))/ε), which is known to be tight (Steinke and Ullman, 2016). A parallel work by Dagan and Kur (2020) provides a similar result, albeit via a completely different approach. One difference between our work and theirs is that our guarantee holds even when δ < 2^−Ω(k/(log k)^8) whereas theirs does not apply in this case. On the other hand, the algorithm of Dagan and Kur has a remarkable advantage that the ℓ∞ error bound of O(sqrt(k ln(1/δ))/ε) holds not only in expectation but always (i.e., with probability one) while we can only get a high probability (or expected) guarantee on the error. View details
    Preview abstract We study the task of differentially private clustering. For several basic clustering problems, including Euclidean DensestBall, 1-Cluster, k-means, and k-median, we give efficient differentially private algorithms that achieve essentially the same approximation ratios as those that can be obtained by any non-private algorithm, while incurring only small additive errors. This improves upon existing efficient algorithms that only achieve some large constant approximation factors. Our results also imply an improved algorithm for the Sample and Aggregate privacy framework. Furthermore, we show that one of the tools used in our 1-Cluster algorithm can be employed to get a faster quantum algorithm for ClosestPair in a moderate number of dimensions. View details
    Preview abstract Differential privacy (DP) is a formal notion for quantifying the privacy loss of algorithms. Algorithms in the central model of DP achieve high accuracy but make the strongest trust assumptions whereas those in the local DP model make the weakest trust assumptions but incur substantial accuracy loss. The shuffled DP model (Bittau et al., 2017; Erlingsson et al., 2019; Cheu et al.,2019) has recently emerged as a feasible middle ground between the central and local models, providing stronger trust assumptions than the former while promising higher accuracies than the latter. In this paper, we obtain practical communication-efficient algorithms in the shuffled DP model for two basic aggregation primitives used in machine learning: 1) binary summation, and 2) histograms over a moderate number of buckets. Our algorithms achieve accuracy that is arbitrarily close to that of central DP algorithms with an expected communication per user essentially matching what is needed without any privacy constraints! We demonstrate the practicality of our algorithms by experimentally comparing their performance to several widely-used protocols such as Randomized Response (Warner, 1965) and RAPPOR (Erlingsson et al., 2014). View details
    Fair Correlation clustering
    23rd International Conference on Artificial Intelligence and Statistics (AISTATS 2020) (2020) (to appear)
    Preview abstract In this paper, we study correlation clustering under fairness constraints. Fair variants of k-median and k-center clustering have been studied recently, and approximation algorithms using a notion called fairlet decomposition have been proposed. We obtain approximation algorithms for fair correlation clustering under several important types of fairness constraints. Our results hinge on obtaining a fairlet decomposition for correlation clustering by introducing a novel combinatorial optimization problem. We define a fairlet decomposition with cost similar to the k-median cost and this allows us to obtain approximation algorithms for a wide range of fairness constraints. We complement our theoretical results with an in-depth analysis of our algorithms on real graphs where we show that fair solutions to correlation clustering can be obtained with limited increase in cost compared to the state-of-the-art (unfair) algorithms. View details
    Preview abstract As machine learning has become more and more integrated into our businesses and lifestyles, researchers have begun to recognize the necessity of ensuring machine learning systems are fair. Recently, there has been an interest in defining a notion of fairness that mitigates over-representation in traditional clustering. In this paper we extend this notion to hierarchical clustering, where the goal is to recursively partition the data to optimize a certain objective~\cite{dasgupta}. For various natural objectives, we obtain simple, efficient algorithms to find a provably good fair hierarchical clustering. Empirically, we show that our algorithms can find a fair hierarchical clustering, surprisingly, with only a negligible loss in the objective. View details
    Pure Differentially Private Summation from Anonymous Messages
    Noah Golowich
    Rasmus Pagh
    Information Theoretic Cryptography (ITC) (2020), 15:1-15:23
    Preview abstract The shuffled (aka anonymous) model has recently generated significant interest as a candidate dis- tributed privacy framework with trust assumptions better than the central model but with achievable error rates smaller than the local model. In this paper, we study pure differentially private protocols in the shuffled model for summation, a very basic and widely used primitive. Specifically: • For the binary summation problem where each of n users holds a bit as an input, we give a pure ε- differentially private protocol for estimating the number of ones held by the users up to an absolute error of Oε(1), and where each user sends Oε(logn) messages each consisting of a single bit. This √ is the first pure differentially private protocol in the shuffled model with error o( n) for constant values of ε. Using our binary summation protocol as a building block, we give a pure ε-differentially private protocol that performs summation of real numbers (in [0,1]) up to an absolute error of Oε(1), and where each user sends Oε(log3 n) messages each consisting of O(loglogn) bits. • In contrast, we show that for any pure ε-differentially private protocol for binary summation in the shuffled model having absolute error n0.5−Ω(1), the per user communication has to be at least Ωε( log n) bits. This implies (i) the first separation between the (bounded-communication) multi- message shuffled model and the central model, and (ii) the first separation between pure and approximate differentially private protocols in the shuffled model. Interestingly, over the course of proving our lower bound, we have to consider (a generalization of) the following question which might be of independent interest: given γ ∈ (0, 1), what is the smallest positive integer m for which there exist two random variables X0 and X1 supported on {0, . . . , m} such that (i) the total variation distance between X0 and X1 is at least 1 − γ, and (ii) the moment generating functions of X0 and X1 are within a constant factor of each other everywhere? We show that the answer to this question is m = Θ( View details
    Preview abstract Clustering is a fundamental problem in unsupervised machine learning. In many applications, clustering needs to be performed in presence of additional constraints, such as fairness or diversity constraints. In this paper, we formulate the problem of k-center clustering without over-representation, and propose approximation algorithms to solve the problem, as well as hardness results. We empirically evaluate our clusterings on real-world dataset and show that fairness can be obtained with limited effect on clustering quality. View details
    Preview abstract The desire to use machine learning to assist in human decision making has spawned a large area of research in understanding the impact of such systems not only on the society as a whole, but also the specific impact on different subpopulations. Recent work has shown that while there are several natural ways to quantify the fairness of a particular system, none of them are universal, and except for trivial cases, satisfying one means violating another~\citet{Kleinberg, Goel, Kleinberg2}. In parallel to understanding the interplay between different definitions of fairness, researchers have looked to develop algorithms for finding fair solutions to specific classes of problems. For example, there is recent work on fair regression, fair clustering, fair bandit algorithms and many others. In this work we tackle another large class of problems that form a useful primitive in machine learning and optimization, that of optimizing a set function subject to a set of matroid constraints. A matroid is a combinatorial object that generalizes linear independence between vectors and is general enough to encode cardinality constraints (e.g. selecting at most $k$ elements), connectivity constraints (e.g. selecting a spanning tree of a graph), or matching constraints (ensuring a subgraph has a perfect matching). View details
    Preview abstract In this paper we introduce the semi-online model that generalizes the classical online computational model. The semi-online model postulates that the unknown future has a predictable part and an adversarial part; these parts can be arbitrarily interleaved. An algorithm in this model operates as in the standard online model, i.e., makes an irrevocable decision at each step. We consider bipartite matching in the semi-online model. Our main contributions are competitive algorithms for this problem and a near-matching hardness bound. The competitive ratio of the algorithms nicely interpolates between the truly offline setting (i.e., no adversarial part) and the truly online setting (i.e., no predictable part). View details
    Preview abstract In this paper we study the well-known family of Random Utility Models, developed over 50 years ago to codify rational user behavior in choosing one item from a finite set of options. In this setting each user draws i.i.d. from some distribution a utility function mapping each item in the universe to a real-valued utility. The user is then offered a subset of the items, and selects the one of maximum utility. A Max-Dist oracle for this choice model takes any subset of items and returns the probability (over the distribution of utility functions) that each will be selected. A discrete choice algorithm, given access to a Max-Dist oracle, must return a function that approximates the oracle. We show three primary results. First, we show that any algorithm exactly reproducing the oracle must make exponentially many queries. Second, we show an equivalent representation of the distribution over utility functions, based on permutations, and show that if this distribution has support size k, then it is possible to approximate the oracle using O(nk) queries. Finally, we consider settings in which the subset of items is always small. We give an algorithm that makes less than n^{(1–∊/2)K} queries, each to sets of size at most (1–∊/2)K, in order to approximate the Max-Dist oracle on every set of size |T| ≤ K with statistical error at most ∊. In contrast, we show that any algorithm that queries for subsets of size 2^{O(sqrt{log n})} must make maximal statistical error on some large sets. View details
    Preview abstract In this work we study the problem of using machine-learned predictions to improve performance of online algorithms. We consider two classical problems, ski rental and non-clairvoyant job scheduling, and obtain new online algorithms that use predictions to make their decisions. These algorithms are oblivious to the performance of the predictor, improve with better predictions, but do not degrade much if the predictions are poor. View details
    Mallows Models for Top-k Lists
    Flavio Chierichetti
    Anirban Dasgupta
    Shahrzad Haddadan
    NeurIPS (2018)
    Preview abstract The classic Mallows model is a widely-used tool to realize distributions on per- mutations. Motivated by common practical situations, in this paper, we generalize Mallows to model distributions on top-k lists by using a suitable distance measure between top-k lists. Unlike many earlier works, our model is both analytically tractable and computationally efficient. We demonstrate this by studying two basic problems in this model, namely, sampling and reconstruction, from both algorithmic and experimental points of view. View details
    Preview abstract The classical Multinomial Logit (MNL) is a behavioral model for user choice. In this model, a user is offered a slate of choices (a subset of a finite universe of n items), and selects exactly one item from the slate, each with probability proportional to its (positive) weight. Given a set of observed slates and choices, the likelihood-maximizing item weights are easy to learn at scale, and easy to interpret. However, the model fails to represent common real-world behavior. As a result, researchers in user choice often turn to mixtures of MNLs, which are known to approximate a large class of models of rational user behavior. Unfortunately, the only known algorithms for this problem have been heuristic in nature. In this paper we give the first polynomial-time algorithms for exact learning of uniform mixtures of two MNLs. Interestingly, the parameters of the model can be learned for any n by sampling the behavior of random users only on slates of sizes 2 and 3; in contrast, we show that slates of size 2 are insufficient by themselves. View details
    Preview abstract We study the question of fair clustering under the disparate impact doctrine, where each protected class must have approximately equal representation in every cluster. We formulate the fair clustering problem under both the k-center and the k-median objectives, and show that even with two protected classes the problem is challenging, as the optimum solution can violate common conventions—for instance a point may no longer be assigned to its nearest cluster center! En route we introduce the concept of fairlets, which are minimal sets that satisfy fair representation while approximately preserving the clustering objective. We show that any fair clustering problem can be decomposed into first finding good fairlets, and then using existing machinery for traditional clustering algorithms. While finding good fairlets can be NP-hard, we proceed to obtain efficient approximation algorithms based on minimum cost flow. We empirically quantify the value of fair clustering on real-world datasets with sensitive attributes. View details
    Partitioning Orders in Online Shopping Services
    Debmalya Panigrahi
    Conf. on Information and Knowledge Management (CIKM) (2017)
    Preview abstract The rapid growth of the sharing economy has led to the widespread use of newer and richer models of online shopping and delivery services. The race to deliver fast has transformed such services into complex networks of shoppers, stores, and consumers. Needless to say, the efficiency of the store order management is critical to the business. Motivated by this setting, we consider the following problem: given a set of online shopping orders each consisting of a few items, how to best partition the orders among a given number of pickers? Owing to logistical constraints the orders are typically unsplittable in the partition. This partitioning, taking the physical location of the items in the store , has to optimize the utilization and amount of work done by the shoppers in the store. Formulating this as a combinatorial optimization problem, we propose a family of simple and efficient algorithms that admit natural constraints arising in this setting. In addition to showing provable guarantees for the algorithms, we also demonstrate their efficiency in practice on real-world data from Google Express [1], outperforming natural baselines. View details
    Preview abstract We consider the problem of approximating a given matrix by a low-rank matrix so as to minimize the entrywise ℓp-approximation error, for any p≥1; the case p=2 is the classical SVD problem. We obtain the first provably good approximation algorithms for this version of low-rank approximation that work for every value of p≥1, including p=∞. Our algorithms are simple, easy to implement, work well in practice, and illustrate interesting tradeoffs between the approximation quality, the running time, and the rank of the approximating matrix. View details
    Caching with Dual Costs
    Anirban Dasgupta
    Proceedings of the 26th International Conference on World Wide Web Companion (2017), pp. 643-652
    Preview abstract Caching mechanisms in distributed and social settings face the issue that the items can frequently change, requiring the cached ver- sions to be updated to maintain coherence. There is thus a trade-off between incurring cache misses on read requests and cache hits on update requests. Motivated by this we consider the following dual cost variant of the classical caching problem: each request for an item can be either a read or a write. If the request is read and the item is not in the cache, then a read-miss cost is incurred and if the request is write and the item is in the cache, then a write-hit cost is incurred. The goal is to design a caching algorithm that minimizes the sum of read-miss and write-hit costs. We study online and offline algorithms for this problem. For the online version of the problem, we obtain an efficient algorithm whose cost is provably close to near-optimal cost. This algorithm builds on online algorithms for classical caching and metrical task systems, using them as black boxes. For the offline ver- sion, we obtain an optimal deterministic algorithm that is based on a minimum cost flow. Experiments on real and synthetic data show that our online algorithm incurs much less cost compared to natural baselines, while utilizing cache even better; furthermore, they also show that the online algorithm is close to the offline optimum. View details
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