Sreenivas Gollapudi
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We study the existence of almost fair and near-optimal solutions to a routing problem as defined in the seminal work of Rosenthal. We focus on the setting where multiple alternative routes are available for each potential request (which corresponds to a potential user of the network). This model captures a collection of diverse applications such as packet routing in communication networks, routing in road networks with multiple alternative routes, and the economics of transportation of goods.
Our recommended routes have provable guarantees in terms of both the total cost and fairness concepts such as approximate envy-freeness. We employ and appropriately combine tools from algorithmic game theory and fair division. Our results apply on two distinct models: the splittable case where the request is split among the selected paths (e.g., routing a fleet of trucks) and the unsplittable case where the request is assigned to one of its designated paths (e.g., a single user request). Finally, we conduct an empirical analysis to test the performance of our approach against simpler baselines using the real world road network of New York City.
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Algorithms for the computation of alternative routes in road networks power many geographic navigation systems. A good set of alternative routes offers meaningful options to the user of the system and can support applications such as routing that is robust to failures (e.g., road closures, extreme traffic congestion, etc.) and routing with diverse preferences and objective functions. Algorithmic techniques for alternative route computation include the penalty method, via-node type algorithms (which deploy bidirectional search and finding plateaus), and, more recently, electrical-circuit based algorithms. In this work we focus on the practically important family of via-node type algorithms and we aim to produce high quality alternative routes for road netowrks. We study alternative route computation in the presence of a fast routing infrastructure that relies on hierarchical routing (namely, CRP). We propose new approaches that rely on deep learning methods. Our training methodology utilizes the hierarchical partition of the graph and builds models to predict which boundary road segments in the partition should be crossed by the alternative routes. We describe our methods in detail and evaluate them against the previously studied architectures, as well as against a stronger baseline that we define in this work, showing improvements in quality in the road networks of Seattle, Paris, and Bangalore.
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Data Exchange Markets via Utility Balancing
Aditya Bhaskara
Sungjin Im
Kamesh Munagala
Govind S. Sankar
WebConf (2024)
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This paper explores the design of a balanced data-sharing marketplace for entities with heterogeneous datasets and machine learning models that they seek to refine using data from other agents. The goal of the marketplace is to encourage participation for data sharing in the presence of such heterogeneity. Our market design approach for data sharing focuses on interim utility balance, where participants contribute and receive equitable utility from refinement of their models. We present such a market model for which we study computational complexity, solution existence, and approximation algorithms for welfare maximization and core stability. We finally support our theoretical insights with simulations on a mean estimation task inspired by road traffic delay estimation.
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Historically, much of machine learning research has focused on the performance of the algorithm alone, but recently more attention has been focused on optimizing joint human-algorithm performance. Here, we analyze a specific type of human-algorithm collaboration where the algorithm has access to a set of $n$ items, and presents a subset of size $k$ to the human, who selects a final item from among those $k$. This scenario could model content recommendation, route planning, or any type of labeling task. Because both the human and algorithm have imperfect, noisy information about the true ordering of items, the key question is: which value of $k$ maximizes the probability that the best item will be ultimately selected? For $k=1$, performance is optimized by the algorithm acting alone, and for $k=n$ it is optimized by the human acting alone.
Surprisingly, we show that for multiple of noise models, it is optimal to set $k \in [2, n-1]$ - that is, there are strict benefits to collaborating, even when the human and algorithm have equal accuracy separately. We demonstrate this theoretically for the Mallows model and experimentally for the Random Utilities models of noisy permutations. However, we show this pattern is \emph{reversed} when the human is anchored on the algorithm's presented ordering - the joint system always has strictly worse performance. We extend these results to the case where the human and algorithm differ in their accuracy levels, showing that there always exist regimes where a more accurate agent would strictly benefit from collaborating with a less accurate one, but these regimes are asymmetric between the human and the algorithm's accuracy.
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Efficient Location Sampling Algorithms for Road Networks
Vivek Kumar
Ameya Velingker
Santhoshini Velusamy
WebConf (2024)
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Many geographic information systems applications rely on the data provided by user devices in the road network. Such applications include traffic monitoring, driving navigation, detecting road closures or the construction of new roads, etc. This signal is collected by sampling locations from the user trajectories and is a critical process for all such systems. Yet, it has not been sufficiently studied in the literature. The most natural way to sample a trajectory is perhaps using a frequency based algorithm, e.g., sample every $x$ seconds. However, as we argue in this paper, such a simple strategy can be very wasteful in terms of resources (e.g., server-side processing, user battery) and in terms of the amount of user data that it maintains. In this work we conduct a horizontal study of various location sampling algorithms (including frequency-based, road geography-based, reservoir-sampling based, etc.) and extract their trade-offs in terms of various metrics of interest, such as, the size of the stored data and the induced quality of training for prediction tasks (e.g., predicting speeds) using the road network of New York City.
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First Passage Percolation with Queried Hints
Kritkorn Karntikoon
Aaron Schild
Yiheng Shen
Ali Sinop
AISTATS (2024)
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Optimization problems are ubiquitous throughout the modern world. In many of these applications, the input is inherently noisy and it is expensive to probe all of the noise in the input before solving the relevant optimization problem. In this work, we study how much of that noise needs to be queried in order to obtain an approximately optimal solution to the relevant problem. We focus on the shortest path problem in graphs, where one may think of the noise as coming from real-time traffic. We consider the following model: start with a weighted base graph $G$ and multiply each edge weight by an independently chosen, uniformly random number in $[1,2]$ to obtain a random graph $G'$. This model is called \emph{first passage percolation}. Mathematicians have studied this model extensively when $G$ is a $d$-dimensional grid graph, but the behavior of shortest paths in this model is still poorly understood in general graphs. We make progress in this direction for a class of graphs that resembles real-world road networks. Specifically, we prove that if the geometric realization of $G$ has constant doubling dimension, then for a given $s-t$ pair, we only need to probe the weights on $((\log n) / \epsilon)^{O(1)}$ edges in $G'$ in order to obtain a $(1 + \epsilon)$-approximation to the $s-t$ distance in $G'$. We also demonstrate experimentally that this result is pessimistic -- one can even obtain a short path in $G'$ with a small number of probes to $G'$.
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We develop an online learning algorithm for a navigation platform to route travelers in a congested network with multiple origin-destination (o-d) pairs while simultaneously learning the unknown cost function of road segments (edges) using the crowd-sourced data. The number of travel requests is randomly realized, and the travel time of each edge is stochastically distributed with the mean being a linear function that increases with the edge load (the number of travelers who take the edge). In each step of our algorithm, the platform updates the estimates of cost function parameters using the collected travel time data, and maintains a rectangular confidence interval of each parameter. The platform then routes travelers in the next step using an optimistic strategy based on the lower bound of the up-to-date confidence interval. The key aspect of our setting is that the number of collected data on each edge depends on the number of travelers who use it, which creates the dependency between the spatial distribution of data points and the routing strategy. We prove that the regret upper bound of our algorithm is \(O(\sqrt{T}\log(T),|E|)\), where \(T\) is the time horizon, and \(|E|\) is the number of edges in the network. Furthermore, we show that the regret bound decreases as the number of travelers increases, which implies that the platform learns faster with a larger user population. Finally, we implement our algorithm on the network of New York City, and demonstrate the efficacy using the accumulated regret.
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Graph Neural Networks (GNNs) have emerged as a powerful technique for learning on relational data. Owing to the relatively limited number of message passing steps they perform—and hence a smaller receptive field—there has been significant interest in improving their expressivity by incorporating structural aspects of the underlying graph. In this paper, we explore the use of affinity measures as features in graph neural networks, in particular measures arising from random walks, including effective resistance, hitting and commute times. We propose message passing networks based on these features and evaluate their performance on a variety of node and graph property prediction tasks. Our architecture has low computational complexity, while our features are invariant to the permutations of the underlying graph. The measures we compute allow the network to exploit the connectivity properties of the graph, thereby allowing us to outperform relevant benchmarks for a wide variety of tasks, often with significantly fewer message passing steps. On one of the largest publicly available graph regression datasets, OGB-LSC-PCQM4Mv1, we obtain the best known single-model validation MAE at the time of writing.
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We consider the classic stochastic multi-armed bandit (MAB) problem, when at each step, the online policy is given the extra power to probe (or observe) the rewards of $k$ arms before playing one of them. We derive new algorithms whose regret bounds in this model have exponentially better dependence on the time horizon when compared to the classic regret bounds. In particular, we show that $k=3$ probes suffice to achieve parameter-independent constant regret of $O(n^2)$, where $n$ is the number of arms. Such regret bounds cannot be achieved even with full feedback {\em after} the play (that is, in the experts model), showcasing the power of even a few probes {\em before} making the play. We present simulations that show benefit of our policies even on benign instances.
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