This paper is part of an emerging line of work at the intersection of machine learning and mechanism design, which aims to avoid noise in training data by correctly aligning the incentives of data sources. Specifically, we focus on the ubiquitous problem of linear regression, where strategyproof mechanisms have previously been identified in two dimensions. In our setting, agents have single-peaked preferences and can manipulate only their response variables. Our main contribution is the discovery of a family of group strategyproof linear regression mechanisms in any number of dimensions, which we call generalized resistant hyperplane mechanisms. The game-theoretic properties of these mechanisms -and, in fact, their very existence -are established through a connection to a discrete version of the Ham Sandwich Theorem.

We address online learning in complex auction settings, such as sponsored search auctions, where the value of the bidder is unknown to her, evolving in an arbitrary manner and observed only if the bidder wins an allocation. We leverage the structure of the utility of the bidder and the partial feedback that bidders typically receive in auctions, in order to provide algorithms with regret rates against the best fixed bid in hindsight, that are exponentially faster in convergence in terms of dependence on the action space, than what would have been derived by applying a generic bandit algorithm and almost equivalent to what would have been achieved in the full information setting. Our results are enabled by analyzing a new online learning setting with outcome-based feedback, which generalizes learning with feedback graphs. We provide an online learning algorithm for this setting, of independent interest, with regret that grows only logarithmically with the number of actions and linearly only in the number of potential outcomes (the latter being very small in most auction settings). Last but not least, we show that our algorithm outperforms the bandit approach experimentally 1 and that this performance is robust to dropping some of our theoretical assumptions or introducing noise in the feedback that the bidder receives.

In this letter, we outline some of the results from our recent work, which is part of an emerging line of research at the intersection of machine learning and mechanism design aiming to avoid noise in training data by correctly aligning the incentives of data sources. Specifically, we focus on the ubiquitous problem of linear regression, where strategyproof mechanisms have previously been identified in two dimensions. In our setting, agents have single-peaked preferences and can manipulate only their response variables. Our main contribution is the discovery of a family of group strategyproof linear regression mechanisms in any number of dimensions, which we call generalized resistant hyperplane mechanisms. The game-theoretic properties of these mechanisms --- and, in fact, their very existence --- are established through a connection to a discrete version of the Ham Sandwich Theorem.

We study a decision-making model where a principal deploys a scoring rule and the agents strategically invest effort to improve their scores. Unlike existing work in the strategic learning literature, we do not assume that the principal's scoring rule is fully known to the agents, and agents may form different estimates of the scoring rule based on their own sources of information. We focus on disparities in outcomes that stem from information discrepancies in our model. To do so, we consider a population of agents who belong to different subgroups, which determine their knowledge about the deployed scoring rule. Agents within each subgroup observe the past scores received by their peers, which allow them to construct an estimate of the deployed scoring rule and to invest their efforts accordingly. The principal, taking into account the agents' behaviors, deploys a scoring rule that maximizes the social welfare of the whole population. We provide a collection of theoretical results that characterize the impact of the welfare-maximizing scoring rules on the strategic effort investments across different subgroups.In particular, we identify sufficient and necessary conditions for when the deployed scoring rule incentivizes optimal strategic investment across all groups for different notions of optimality. Finally, we complement and validate our theoretical analysis with experimental results on the real-world datasets Taiwan-Credit and Adult.

Standard game-theoretic formulations for settings like contextual pricing and security games assume that agents act in accordance with a specific behavioral model. In practice however, some agents may not prescribe to the dominant behavioral model or may act in ways that are arbitrarily inconsistent. Existing algorithms heavily depend on the model being (approximately) accurate for all agents and have poor performance in the presence of even a few such arbitrarily irrational agents. How do we design learning algorithms that are robust to the presence of arbitrarily irrational agents?We address this question for a number of canonical game-theoretic applications by designing a robust algorithm for the fundamental problem of multidimensional binary search. The performance of our algorithm degrades gracefully with the number of corrupted rounds, which correspond to irrational agents and need not be known in advance. As binary search is the key primitive in algorithms for contextual pricing, Stackelberg Security Games, and other gametheoretic applications, we immediately obtain robust algorithms for these settings.Our techniques draw inspiration from learning theory, game theory, high-dimensional geometry, and convex analysis, and may be of independent algorithmic interest.