Social Aspects of Algorithms: Fairness, Diversity, and Resilience to Strategic Behavior

With algorithms becoming ubiquitous in our society, it is important to ensure that they are compatible with our social values. In this thesis, we study some of the social aspects of algorithms including fairness, diversity, and resilience to strategic behavior of individuals. Lack of diversity has a potential impact on discrimination against marginalized groups. Inspired by this issue, in the first part of this thesis, we study a notion of diversity in bipartite matching problems. Bipartite matching where agents on one side of a market are matched to one or more agents or items on the other side, is a classical model that is used in myriad application areas such as healthcare, advertising, education, and general resource allocation. In particular, we consider an application of matchings where a firm wants to hire, i.e. match, some workers for a number of teams. Each team has a demand that needs to be satisfied, and each worker has multiple features (e.g., country of origin, gender). We ask the question of how to assign workers to the teams in an efficient way, i.e. low-cost matching, while forming diverse teams with respect to all the features. Inspired by previous work, we balance whole-match diversity and economic efficiency by optimizing a supermodular function over the matching. Particularly, we show when the number of features is given as part of the input, this problem is NP-hard, and design a pseudo-polynomial time algorithm to solve this problem. Next, we focus on studying fairness in optimization problems. Particularly, in this thesis, we study two notions of fairness in an optimization problem called correlation clustering. In correlation clustering, given an edge-weighted graph, each edge in addition to a weight has a positive or negative label. The goal is to obtain a clustering of the vertices into an arbitrary number of clusters that minimizes disagreements which is defined as the total weight of negative edges trapped inside a cluster plus the sum of weights of positive edges between different clusters. In the first fairness notion, assuming each node has a color, i.e. feature, our aim is to generate clusters with minimum disagreements, where the distribution of colors in each cluster is the same as the global distribution. Next, we switch our attention to a min-max notion of fairness in correlation clustering. In this notion of fairness, we consider a cluster-wise objective function that asks to minimize the maximum number of disagreements of each cluster. In this notion, the goal is to respect the quality of each cluster. We focus on designing approximation algorithms for both of these notions. In the last part of this thesis, we take into consideration, the vulnerability of algorithms to manipulation and gaming. We study the problem of how to learn a linear classifier in presence of strategic agents that desire to be classified as positive and that are able to modify their position by a limited amount, making the classifier not be able to observe the true position of agents but rather a position where the agent pretends to be. We focus on designing algorithms with a bounded number of mistakes for a few different variations of this problem

Proceedings of the 8th Cologne-Twente Workshop on Graphs and Combinatorial Optimization

International audienceThe Cologne-Twente Workshop (CTW) on Graphs and Combinatorial Optimization started off as a series of workshops organized bi-annually by either Köln University or Twente University. As its importance grew over time, it re-centered its geographical focus by including northern Italy (CTW04 in Menaggio, on the lake Como and CTW08 in Gargnano, on the Garda lake). This year, CTW (in its eighth edition) will be staged in France for the first time: more precisely in the heart of Paris, at the Conservatoire National d’Arts et Métiers (CNAM), between 2nd and 4th June 2009, by a mixed organizing committee with members from LIX, Ecole Polytechnique and CEDRIC, CNAM

LEARNING ON GRAPHS: ALGORITHMS FOR CLASSIFICATION AND SEQUENTIAL DECISIONS

In recent years, networked data have become widespread due to the increasing importance of social networks and other web-related applications. This growing interest is driving researchers to design new algorithms for solving important problems that involve networked data. In this thesis we present a few practical yet principled algorithms for learning and sequential decision-making on graphs. Classification of networked data is an important problem that has recently received a great deal of attention from the machine learning community. This is due to its many important practical applications: computer vision, bioinformatics, spam detection and text categorization, just to cite a few of the more conspicuous examples. We focus our attention on the task called ``node classification'', often studied in the semi-supervised (transductive) setting. We present two algorithms, motivated by different theoretical frameworks. The first algorithm is studied in the well-known online adversarial setting, within which it enjoys an optimal mistake bound (up to logarithmic factors). The second algorithm is based on a game-theoretic approach, where each node of the network is maximizing its own payoff. The setting corresponds to a Graph Transduction Game in which the graph is a tree. For this special case, we show that the Nash Equilibrium of the game can be reached in linear time. We complement our theoretical findings with an extensive set of experiments using datasets from many different domains. In the second part of the thesis, we present a rapidly emerging theme in the analysis of networked data: signed networks, graphs whose edges carry a label encoding the positive or negative nature of the relationship between the connected nodes. For example, social networks and e-commerce offer several examples of signed relationships: Slashdot users can tag other users as friends or foes, Epinions users can rate each other positively or negatively, Ebay users develop trust and distrust towards sellers in the network. More generally, two individuals that are related because they rate similar products in a recommendation website may agree or disagree in their ratings. Many heuristics for link classification in social networks are based on a form of social balance summarized by the motto \u201cthe enemy of my enemy is my friend\u201d. This is equivalent to saying that the signs on the edges of a social graph tend to be consistent with some two-clustering structure of the nodes, where edges connecting nodes from the same cluster are positive and edges connecting nodes from different clusters are negative. We present algorithms for the batch transductive active learning setting, where the topology of the graph is known in advance and our algorithms can ask for the label of some specific edges during the training phase (before starting with the predictions). These algorithms can achieve different tradeoffs between the number of mistakes during the test phase and the number of labels required during the training phase. We also presented an experimental comparison against some state-of-the-art spectral heuristics presented in a previous work, where we show that the simplest or our algorithms is already competitive with the best of these heuristics. In the last chapter we present another way to exploit relational information for sequential predictions: the networks of bandits. Contextual bandits adequately formalize the exploration-exploitation trade-offs arising in several industrially relevant applications, such online advertisement and recommendation systems. Many practical applications have a strong social component whose integration in the bandit algorithm could lead to a significant performance improvement: for example, since often friends have similar taste, we may want to serve contents to a group of users by taking advantage of an underlying network of social relationships among them. We introduce a novel algorithmic approach to a particular networked bandit problem. More specifically, we run a bandit algorithm on each network node (e.g., user), allowing it to ``share'' feedback signals with the other nodes by employing the multi-task kernel. We derive the regret analysis of this algorithm and, finally, we report on the results of an experimental comparison between our approach and the state of the art techniques, on both artificial and real-world social networks

Mechanism Design For Covering Problems

Algorithmic mechanism design deals with efficiently-computable algorithmic constructions in the presence of strategic players who hold the inputs to the problem and may misreport their input if doing so benefits them. Algorithmic mechanism design finds applications in a variety of internet settings such as resource allocation, facility location and e-commerce, such as sponsored search auctions. There is an extensive amount of work in algorithmic mechanism design on packing problems such as single-item auctions, multi-unit auctions and combinatorial auctions. But, surprisingly, covering problems, also called procurement auctions, have almost been completely unexplored, especially in the multidimensional setting. In this thesis, we systematically investigate multidimensional covering mechanism- design problems, wherein there are m items that need to be covered and n players who provide covering objects, with each player i having a private cost for the covering objects he provides. A feasible solution to the covering problem is a collection of covering objects (obtained from the various players) that together cover all items. Two widely considered objectives in mechanism design are: (i) cost-minimization (CM) which aims to minimize the total cost incurred by the players and the mechanism designer; and (ii) payment minimization (PayM), which aims to minimize the payment to players. Covering mechanism design problems turn out to behave quite differently from packing mechanism design problems. In particular, various techniques utilized successfully for packing problems do not perform well for covering mechanism design problems, and this necessitates new approaches and solution concepts. In this thesis we devise various techniques for handling covering mechanism design problems, which yield a variety of results for both the CM and PayM objectives. In our investigation of the CM objective, we focus on two representative covering problems: uncapacitated facility location (UFL) and vertex cover. For multi-dimensional UFL, we give a black-box method to transform any Lagrangian-multiplier-preserving ρ-approximation algorithm for UFL into a truthful-in-expectation, ρ-approximation mechanism. This yields the first result for multi-dimensional UFL, namely a truthful-in-expectation 2-approximation mechanism. For multi-dimensional VCP (Multi-VCP), we develop a decomposition method that reduces the mechanism-design problem into the simpler task of constructing threshold mechanisms, which are a restricted class of truthful mechanisms, for simpler (in terms of graph structure or problem dimension) instances of Multi-VCP. By suitably designing the decomposition and the threshold mechanisms it uses as building blocks, we obtain truthful mechanisms with approximation ratios (n is the number of nodes): (1) O(r2 log n) for r-dimensional VCP; and (2) O(r log n) for r-dimensional VCP on any proper minor-closed family of graphs (which improves to O(log n) if no two neighbors of a node belong to the same player). These are the first truthful mechanisms for Multi-VCP with non-trivial approximation guarantees. For the PayM objective, we work in the oft-used Bayesian setting, where players’ types are drawn from an underlying distribution and may be correlated, and the goal is to minimize the expected total payment made by the mechanism. We consider the problem of designing incentive compatible, ex-post individually rational (IR) mechanisms for covering problems in the above model. The standard notion of incentive compatibility (IC) in such settings is Bayesian incentive compatibility (BIC), but this notion is over-reliant on having precise knowledge of the underlying distribution, which makes it a rather non- robust notion. We formulate a notion of IC that we call robust Bayesian IC (robust BIC) that is substantially more robust than BIC, and develop black-box reductions from robust BIC-mechanism design to algorithm design. This black-box reduction applies to single- dimensional settings even when we only have an LP-relative approximation algorithm for the algorithmic problem. We obtain near-optimal mechanisms for various covering settings including single- and multi-item procurement auctions, various single-dimensional covering problems, and multidimensional facility location problems. Finally, we study the notion of frugality, which considers the PayM objective but in a worst-case setting, where one does not have prior information about the players’ types. We show that some of our mechanisms developed for the CM objective are also good with respect to certain oft-used frugality benchmarks proposed in the literature. We also introduce an alternate benchmark for frugality, which more directly reflects the goal that the mechanism’s payment be close to the best possible payment, and obtain some preliminary results with respect to this benchmark

LIPIcs, Volume 251, ITCS 2023, Complete Volume

LIPIcs, Volume 251, ITCS 2023, Complete Volum

LIPIcs, Volume 261, ICALP 2023, Complete Volume

LIPIcs, Volume 261, ICALP 2023, Complete Volum