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Reward learning as a method for inferring human intent and preferences has been studied extensively. Prior approaches make an implicit assumption that the human maintains a correct belief about the robot's domain dynamics. However, this may not always hold since the human's belief may be biased, which can ultimately lead to a misguided estimation of the human's intent and preferences, which is often derived from human feedback on the robot's behaviors. In this paper, we remove this restrictive assumption by considering that the human may have an inaccurate understanding of the robot. We propose a method called Generalized Reward Learning with biased beliefs about domain dynamics (GeReL) to infer both the reward function and human's belief about the robot in a Bayesian setting based on human ratings. Due to the complex forms of the posteriors, we formulate it as a variational inference problem to infer the posteriors of the parameters that govern the reward function and human's belief about the robot simultaneously. We evaluate our method in a simulated domain and with a user study where the user has a bias based on the robot's appearances. The results show that our method can recover the true human preferences while subject to such biased beliefs, in contrast to prior approaches that could have misinterpreted them completely. 

Almost all of the work in graphical models for game theory has mirrored previous work in probabilistic graphical models. Our work considers the opposite direction: Taking advantage of advances in equilibrium computation for probabilistic inference. In particular, we present formulations of inference problems in Markov random fields (MRFs) as computation of equilibria in a certain class of game-theoretic graphical models. While some previous work explores this direction, we still lack a more precise connection between variational probabilistic inference in MRFs and correlated equilibria. This paper sharpens the connection, which helps us exploit relatively more recent theoretical and empirical results from the literature on algorithmic and computational game theory on the tractable, polynomial-time computation of exact or approximate correlated equilibria in graphical games with arbitrary, loopy graph structure. Our work discusses how to design new algorithms with equally tractable guarantees for the computation of approximate variational inference in MRFs. In addition, inspired by a previously stated game-theoretic view of tree-reweighted message-passing techniques for belief inference as a zero-sum game, we propose a different, general-sum potential game to design approximate fictitious-play techniques. Empirical evaluations on synthetic experiments and on an application to soft de-noising on real-world image datasets illustrate the performance of our proposed approach and shed some light on the conditions under which the resulting belief inference algorithms may be most effective relative to standard state-of-the-art methods.