We study a hinted heterogeneous multi-agent multi-armed bandits problem (HMA2B), where agents can query low-cost observations (hints) in addition to pulling arms. In this framework, each of the M agents has a unique reward distribution over K arms, and in T rounds, they can observe the reward of the arm they pull only if no other agent pulls that arm. The goal is to maximize the total utility by querying the minimal necessary hints without pulling arms, achieving time-independent regret. We study HMA2B in both centralized and decentralized setups. Our main centralized algorithm, GP-HCLA, which is an extension of HCLA, uses a central decision-maker for arm-pulling and hint queries, achieving O(M^4 K) regret with O(M K log T) adaptive hints. In decentralized setups, we propose two algorithms, HD-ETC and EBHD-ETC, that allow agents to choose actions independently through collision-based communication and query hints uniformly until stopping, yielding O(M^3 K^2) regret with O(M^3 K log T) hints, where the former requires knowledge of the minimum gap and the latter does not. Finally, we establish lower bounds to prove the optimality of our results and verify them through numerical simulations.

Numerous works propose post-hoc, model-agnostic explanations for learning to rank, focusing on ordering entities by their relevance to a query through feature attribution methods. However, these attributions often weakly correlate or contradict each other, confusing end users. We adopt an axiomatic game-theoretic approach, popular in the feature attribution community, to identify a set of fundamental axioms that every ranking-based feature attribution method should satisfy. We then introduce Rank-SHAP, extending classical Shapley values to ranking. We evaluate the RankSHAP framework through extensive experiments on two datasets, multiple ranking methods and evaluation metrics. Additionally, a user study confirms RankSHAP’s alignment with human intuition. We also perform an axiomatic analysis of existing rank attribution algorithms to determine their compliance with our proposed axioms. Ultimately, our aim is to equip practitioners with a set of axiomatically backed feature attribution methods for studying IR ranking models, that ensure generality as well as consistency.

The recent criticisms of the robustness of post hoc model approximation explanation methods (like LIME and SHAP) have led to the rise of model-precise abductive explanations. For each data point, abductive explanations provide a minimal subset of features that are sufficient to generate the outcome. While theoretically sound and rigorous, abductive explanations suffer from a major issue --- there can be several valid abductive explanations for the same data point. In such cases, providing a single abductive explanation can be insufficient; on the other hand, providing all valid abductive explanations can be incomprehensible due to their size. In this work, we solve this issue by aggregating the many possible abductive explanations into feature importance scores. We propose three aggregation methods: two based on power indices from cooperative game theory and a third based on a well-known measure of causal strength. We characterize these three methods axiomatically, showing that each of them uniquely satisfies a set of desirable properties. We also evaluate them on multiple datasets and show that these explanations are robust to the attacks that fool SHAP and LIME.

We study fair allocation of constrained resources, where a market designer optimizes overall welfare while maintaining group fairness. In many large-scale settings, utilities are not known in advance, but are instead observed after realizing the allocation. We therefore estimate agent utilities using machine learning. Optimizing over estimates requires trading-off between mean utilities and their predictive variances. We discuss these trade-offs under two paradigms for preference modeling – in the stochastic optimization regime, the market designer has access to a probability distribution over utilities, and in the robust optimization regime they have access to an uncertainty set containing the true utilities with high probability. We discuss utilitarian and egalitarian welfare objectives, and we explore how to optimize for them under stochastic and robust paradigms. We demonstrate the efficacy of our approaches on three publicly available conference reviewer assignment datasets. The approaches presented enable scalable constrained resource allocation under uncertainty for many combinations of objectives and preference models.

In reinforcement learning, robust policies for high-stakes decision-making problems with limited data are usually computed by optimizing the percentile criterion. The percentile criterion is optimized by constructing an uncertainty set that contains the true model with high probability and optimizing the policy for the worst model in the set. Since the percentile criterion is non-convex, constructing these sets itself is challenging. Existing works use Bayesian credible regions as uncertainty sets, but they are often unnecessarily large and result in learning overly conservative policies. To overcome these shortcomings, we propose a novel Value-at-Risk based dynamic programming algorithm to optimize the percentile criterion without explicitly constructing any uncertainty sets. Our theoretical and empirical results show that our algorithm implicitly constructs much smaller uncertainty sets and learns less-conservative robust policies.

We study the problem of fairly allocating a set of indivisible goods among agents with matroid rank valuations --- every good provides a marginal value of 0 or 1 when added to a bundle and valuations are submodular. We generalize the Yankee Swap algorithm to create a simple framework, called General Yankee Swap, that can efficiently compute allocations that maximize any justice criterion (or fairness objective) satisfying some mild assumptions. Along with maximizing a justice criterion, General Yankee Swap is guaranteed to maximize utilitarian social welfare, ensure strategyproofness and use at most a quadratic number of valuation queries. We show how General Yankee Swap can be used to compute allocations for five different well-studied justice criteria: (a) Prioritized Lorenz dominance, (b) Maximin fairness, (c) Weighted leximin, (d) Max weighted Nash welfare, and (e) Max weighted p-mean welfare. In particular, our framework provides the first polynomial time algorithms to compute weighted leximin, max weighted Nash welfare and max weighted p-mean welfare allocations for agents with matroid rank valuations.

We study mechanisms that allocate reviewers to papers in a fair and efficient manner. We model reviewer assignment as an instance of a fair allocation problem, presenting an extension of the classic round-robin mechanism, called Reviewer Round Robin (RRR). Round-robin mechanisms are a standard tool to ensure envy-free up to one item (EF1) allocations. However, fairness often comes at the cost of decreased efficiency. To overcome this challenge, we carefully select an approximately optimal round-robin order. Applying a relaxation of submodularity, γ-weak submodularity, we show that greedily inserting papers into an order yields a (1+γ²)-approximation to the maximum welfare attainable by our round-robin mechanism under any order. Our Greedy Reviewer Round Robin (GRRR) approach outputs highly efficient EF1 allocations for three real conference datasets, offering comparable performance to state-of-the-art paper assignment methods in fairness, efficiency, and runtime, while providing the only EF1 guarantee.

Privacy and transparency are two key foundations of trustworthy machine learning. Model explanations offer insights into a model's decisions on input data, whereas privacy is primarily concerned with protecting information about the training data. We analyze connections between model explanations and the leakage of sensitive information about the model's training set. We investigate the privacy risks of feature-based model explanations using membership inference attacks: quantifying how much model predictions plus their explanations leak information about the presence of a datapoint in the training set of a model. We extensively evaluate membership inference attacks based on feature-based model explanations, over a variety of datasets. We show that backpropagation-based explanations can leak a significant amount of information about individual training datapoints. This is because they reveal statistical information about the decision boundaries of the model about an input, which can reveal its membership. We also empirically investigate the trade-off between privacy and explanation quality, by studying the perturbation-based model explanations.

My research in the past few years has focused on fostering trust in algorithmic systems. I often analyze scenarios where a variety of desirable trust-oriented goals must be simultaneously satisfied; for example, ensuring that an allocation mechanism is both fair and efficient, or that a model explanation framework is both effective and differentially private. This interdisciplinary approach requires tools from a variety of computer science disciplines, such as game theory, economics, ML and differential privacy.

We examine the problem of assigning plots of land to prospective buyers who prefer living next to their friends. In this setting, each agent's utility depends on the plot she receives and the identities of the agents who receive the adjacent plots. We are interested in mechanisms without money that guarantee truthful reporting of both land values and friendships, as well as Pareto optimality and computational efficiency. We explore several modifications of the Random Serial Dictatorship (RSD) mechanism, and identify one that performs well according to these criteria, We also study the expected social welfare of the assignments produced by our mechanisms when agents' values for the land plots are binary; it turns out that we can achieve good approximations to the optimal social welfare, but only if the agents value the friendships highly.

The past few years have seen several works exploring learning economic solutions from data; these include optimal auction design, function optimization, stable payoffs in cooperative games and more. In this work, we provide a unified learning-theoretic methodology for modeling such problems, and establish tools for determining whether a given solution concept can be efficiently learned from data. Our learning theoretic framework generalizes a notion of function space dimension --- the graph dimension --- adapting it to the solution concept learning domain. We identify sufficient conditions for efficient solution learnability, and show that results in existing works can be immediately derived using our methodology. Finally, we apply our methods in other economic domains, yielding learning variants of competitive equilibria and Condorcet winners.

This article proposes a negotiation game, based on the weighted voting paradigm in cooperative game theory, where agents need to form coalitions and agree on how to share the gains. Despite the prevalence of weighted voting in the real world, there has been little work studying people’s behavior in such settings. This work addresses this gap by combining game-theoretic solution concepts with machine learning models for predicting human behavior in such domains. We present a five-player online version of a weighted voting game in which people negotiate to create coalitions. We provide an equilibrium analysis of this game and collect hundreds of instances of people’s play in the game. We show that a machine learning model with features based on solution concepts from cooperative game theory (in particular, an extension of the Deegan-Packel Index) provide a good prediction of people’s decisions to join coalitions in the game. We designed an agent that uses the prediction model to make offers to people in this game and was able to outperform other people in an extensive empirical study. These results demonstrate the benefit of incorporating concepts from cooperative game theory in the design of agents that interact with people in group decision-making settings.

A community needs to be partitioned into disjoint groups; each community member has an underlying preference over the groups that they would want to be a member of. We are interested in finding a stable community structure: one where no subset of members S wants to deviate from the current structure. We model this setting as a hedonic game, where players are connected by an underlying interaction network, and can only consider joining groups that are connected subgraphs of the underlying graph. We analyze the relation between network structure, and one’s capability to infer statistically stable (also known as PAC stable) player partitions from data. We show that when the interaction network is a forest, one can efficiently infer PAC stable coalition structures. Furthermore, when the underlying interaction graph is not a forest, efficient PAC stabilizability is no longer achievable. Thus, our results completely characterize when one can leverage the underlying graph structure in order to compute PAC stable outcomes for hedonic games. Finally, given an unknown underlying interaction network, we show that it is NP-hard to decide whether there exists a forest consistent with data samples from the network.

We study the following problem: given a labeled dataset and a specific datapoint ∼x, how did the i-th feature influence the classification for ∼x? We identify a family of numerical influence measures — functions that, given a datapoint ∼x, assign a numeric value φi(∼x) to every feature i, corresponding to how altering i’s value would influence the outcome for ∼x. This family, which we term monotone influence measures (MIM), is uniquely derived from a set of desirable properties, or axioms. The MIM family constitutes a provably sound methodology for measuring feature influence in classification domains; the values generated by MIM are based on the dataset alone, and do not make any queries to the classifier. While this requirement naturally limits the scope of our framework, we demonstrate its effectiveness on data.

In this paper, we study the problem of matching a set of items to a set of agents partitioned into types so as to balance fairness towards the types against overall utility/efficiency. We extend multiple desirable properties of indivisible goods allocation to our model and investigate the possibility and hardness of achieving combinations of these properties, e.g. we prove that maximizing utilitarian social welfare under constraints of typewise envy-freeness up to one item (TEF1) is computationally intractable. We also define a new concept of waste for this setting, show experimentally that augmenting an existing algorithm with a marginal utility maximization heuristic can produce a TEF1 solution with reduced waste, and also provide a polynomial-time algorithm for computing a non-wasteful TEF1 allocation for binary agent-item utilities.

Influence maximization is a widely used model for information dissemination in social networks. Recent work has employed such interventions across a wide range of social problems, spanning public health, substance abuse, and international development (to name a few examples). A critical but understudied question is whether the benefits of such interventions are fairly distributed across different groups in the population; e.g., avoiding discrimination with respect to sensitive attributes such as race or gender. Drawing on legal and game-theoretic concepts, we introduce formal definitions of fairness in influence maximization. We provide an algorithmic framework to find solutions which satisfy fairness constraints, and in the process improve the state of the art for general multi-objective submodular maximization problems. Experimental results on real data from an HIV prevention intervention for homeless youth show that standard influence maximization techniques oftentimes neglect smaller groups which contribute less to overall utility, resulting in a disparity which our proposed algorithms substantially reduce.

What is a fair way to assign rooms to several housemates, and divide the rent between them? This is not just a theoretical question: many people have used the Spliddit website to obtain envy-free solutions to rent division instances. But envy freeness, in and of itself, is insufficient to guarantee outcomes that people view as intuitive and acceptable. We therefore focus on solutions that optimize a criterion of social justice, subject to the envy freeness constraint, in order to pinpoint the “fairest” solutions. We develop a general algorithmic framework that enables the computation of such solutions in polynomial time. We then study the relations between natural optimization objectives, and identify the maximin solution, which maximizes the minimum utility subject to envy freeness, as the most attractive. We demonstrate, in theory and using experiments on real data from Spliddit, that the maximin solution gives rise to significant gains in terms of our optimization objectives. Finally, a user study with Spliddit users as subjects demonstrates that people find the maximin solution to be significantly fairer than arbitrary envy-free solutions; this user study is unprecedented in that it asks people about their real-world rent division instances. Based on these results, the maximin solution has been deployed on Spliddit since April 2015.

Coalitional stability in hedonic games has usually been considered in the setting where agent preferences are fully known. We consider the setting where agent preferences are unknown; we lay the theoretical foundations for studying the interplay between coalitional stability and (PAC) learning in hedonic games. We introduce the notion of PAC stability - the equivalent of core stability under uncertainty - and examine the PAC stabilizability and learnability of several popular classes of hedonic games.

Despite the prevalence of weighted voting in the real world, there has been relatively little work studying real people's behavior in such settings. This paper proposes a new negotiation game, based on the weighted voting paradigm in cooperative games, where players need to form coalitions and agree on how to share the gains. We show that solution concepts from cooperative game theory (in particular, an extension of the Deegan-Packel Index) provide a good prediction of people's decisions to join a given coalition. With this insight in mind, we design an agent that combines predictive analytics with decision theory to make offers to people in the game. We show that the agent was able to obtain higher shares from coalitions than did people playing other people, without reducing the acceptance rate of its offers. These results demonstrate the potential of incorporating concepts from cooperative game theory in the design of negotiating agents.

“Mirror, mirror, on the wall, who is the fairest of them all?” The Evil Queen What is a fair way to assign rooms to several housemates and divide the rent between them? This is not just a theoretical question: many people have used the Spliddit website to obtain envy-free solutions to rent division instances. But envy freeness, in and of itself, is insufficient to guarantee outcomes that people view as intuitive and acceptable. We therefore focus on solutions that optimize a criterion of social justice, subject to the envy-freeness constraint, in order to pinpoint the “fairest” solutions. We develop a general algorithmic framework that enables the computation of such solutions in polynomial time. We then study the relations between natural optimization objectives and identify the maximin solution, which maximizes the minimum utility subject to envy freeness, as the most attractive. We demonstrate, in theory and using experiments on real data from Spliddit, that the maximin solution gives rise to significant gains in terms of our optimization objectives. Finally, a user study with Spliddit users as subjects demonstrates that people find the maximin solution to be significantly fairer than arbitrary envy-free solutions; this user study is unprecedented in that it asks people about their real-world rent division instances. Based on these results, the maximin solution has been deployed on Spliddit since April 2015.

What is a fair way to assign rooms to several housemates, and divide the rent between them? This is not just a theoretical question: many people have used the Spliddit website to obtain envy-free solutions to rent division instances. But envy freeness, in and of itself, is insufficient to guarantee outcomes that people view as intuitive and acceptable. We therefore focus on solutions that optimize a criterion of social justice, subject to the envy freeness constraint, in order to pinpoint the ``fairest'' solutions. We develop a general algorithmic framework that enables the computation of such solutions in polynomial time. We then study the relations between natural optimization objectives, and identify the maximin solution, which maximizes the minimum utility subject to envy freeness, as the most attractive. We demonstrate, in theory and using experiments on real data from Spliddit, that the maximin solution gives rise to significant gains in terms of our optimization objectives. Finally, a user study with Spliddit users as subjects demonstrates that people find the maximin solution to be significantly fairer than arbitrary envy-free solutions; this user study is unprecedented in that it asks people about their real-world rent division instances. Based on these results, the maximin solution has been deployed on Spliddit since April 2015.

Algorithmic systems that employ machine learning play an increasing role in making substantive decisions in modern society, ranging from online personalization to insurance and credit decisions to predictive policing. But their decision-making processes are often opaque-it is difficult to explain why a certain decision was made. We develop a formal foundation to improve the transparency of such decision-making systems. Specifically, we introduce a family of Quantitative Input Influence (QII) measures that capture the degree of influence of inputs on outputs of systems. These measures provide a foundation for the design of transparency reports that accompany system decisions (e.g., explaining a specific credit decision) and for testing tools useful for internal and external oversight (e.g., to detect algorithmic discrimination). Distinctively, our causal QII measures carefully account for correlated inputs while measuring influence. They support a general class of transparency queries and can, in particular, explain decisions about individuals (e.g., a loan decision) and groups (e.g., disparate impact based on gender). Finally, since single inputs may not always have high influence, the QII measures also quantify the joint influence of a set of inputs (e.g., age and income) on outcomes (e.g. loan decisions) and the marginal influence of individual inputs within such a set (e.g., income). Since a single input may be part of multiple influential sets, the average marginal influence of the input is computed using principled aggregation measures, such as the Shapley value, previously applied to measure influence in voting. Further, since transparency reports could compromise privacy, we explore the transparency-privacy tradeoff and prove that a number of useful transparency reports can be made differentially private with very little addition of noise. Our empirical validation with standard machine learning algorithms demonstrates that QII measures are a useful transparency mechanism when black box access to the learning system is available. In particular, they provide better explanations than standard associative measures for a host of scenarios that we consider. Further, we show that in the situations we consider, QII is efficiently approximable and can be made differentially private while preserving accuracy.

We present the first model of optimal voting under adversarial noise. From this viewpoint, voting rules are seen as error-correcting codes: their goal is to correct errors in the input rankings and recover a ranking that is close to the ground truth. We derive worst-case bounds on the relation between the average accuracy of the input votes, and the accuracy of the output ranking. Empirical results from real data show that our approach produces significantly more accurate rankings than alternative approaches.

Overlapping Coalition Formation (OCF) games, introduced by Chalkiadakis, Elkind, Markakis, Polukarov and Jennings in 2010, are cooperative games where players can simultaneously participate in several coalitions. Capturing the notion of stability in OCF games is a difficult task:deviating players may continue to contribute resources to joint projects with non-deviators, and the crucial question is what payoffs the deviators expect to receive from such projects. Chalkiadakis et al. introduce three stability concepts for OCF games---the conservative core, the refined core, and the optimistic core---that are based on different answers to this question. In this paper, we propose a unified framework for the study of stability in the OCF setting, which encompasses the stability concepts considered by Chalkiadakis et al. as well as a wide variety of alternative stability concepts. Our approach is based on the notion of arbitration functions, which determine the payoff obtained by the deviators, given their deviation and the current allocation of resources. We provide a characterization of stable outcomes under arbitration. We then conduct an in-depth study of four types of arbitration functions, which correspond to four notions of the core; these include the three notions of the core considered by Chalkiadakis et al. Our results complement those of Chalkiadakis et al. and answer questions left open by their work. In particular, we show that OCF games with the conservative arbitration function are essentially equivalent to non-OCF games, by relating the conservative core of an OCF game to the core of a non-overlapping cooperative game, and use this result to obtain a strictly weaker sufficient condition for conservative core non-emptiness than the one given by Chalkiadakis et al.

We study the stability of cooperative games played over an interaction network, in a model that was introduced by Myerson ['77]. We show that the cost of stability of such games (i.e., the subsidy required to stabilize the game) can be bounded in terms of natural parameters of their underlying interaction networks. Specifically, we prove that if the treewidth of the interaction network H is k, then the relative cost of stability of any game played over H is at most k + 1, and if the pathwidth of H is k', then the relative cost of stability is at most k'. We show that these bounds are tight for all k≥ 2and all k' ≥ 1, respectively.

The core is a central solution concept in cooperative game theory, and therefore it is important to know under what conditions the core of a game is guaranteed to be non-empty. Two notions that prove to be very useful in this context are Linear Programming (LP) duality and convexity. In this work, we apply these tools to identify games with overlapping coalitions (OCF games) that admit stable outcomes. We focus on three notions of the core defined in (Chalkiadakis et al. 2010) for such games, namely, the conservative core, the refined core and the optimistic core. First, we show that the conservative core of an OCF game is non-empty if and only if the core of a related classic coalitional game is non-empty. This enables us to improve the result of (Chalkiadakis et al. 2010) by giving a strictly weaker sufficient condition for the non-emptiness of the conservative core. We then use LP duality to characterize OCF games with non-empty refined core; as a corollary, we show that the refined core of a game is non-empty as long as the superadditive cover of its characteristic function is convex. Finally, we identify a large class of OCF games that can be shown to have a non-empty optimistic core using an LP based argument.