A Maximum-Entropy Approach to Off-Policy Evaluation in Average-Reward MDPs

Part of Advances in Neural Information Processing Systems 33 (NeurIPS 2020)

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Authors

Nevena Lazic, Dong Yin, Mehrdad Farajtabar, Nir Levine, Dilan Gorur, Chris Harris, Dale Schuurmans

Abstract

This work focuses on off-policy evaluation (OPE) with function approximation in infinite-horizon undiscounted Markov decision processes (MDPs). For MDPs that are ergodic and linear (i.e. where rewards and dynamics are linear in some known features), we provide the first finite-sample OPE error bound, extending the existing results beyond the episodic and discounted cases. In a more general setting, when the feature dynamics are approximately linear and for arbitrary rewards, we propose a new approach for estimating stationary distributions with function approximation. We formulate this problem as finding the maximum-entropy distribution subject to matching feature expectations under empirical dynamics. We show that this results in an exponential-family distribution whose sufficient statistics are the features, paralleling maximum-entropy approaches in supervised learning. We demonstrate the effectiveness of the proposed OPE approaches in multiple environments.