Off-Policy Exploitability-Evaluation and Equilibrium-Learning in Two-Player Zero-Sum Markov Games

07/04/2020 ∙ by Kenshi Abe, et al. ∙ 0

Off-policy evaluation (OPE) is the problem of evaluating new policies using historical data obtained from a different policy. Off-policy learning (OPL), on the other hand, is the problem of finding an optimal policy using historical data. In recent OPE and OPL contexts, most of the studies have focused on one-player cases, and not on more than two-player cases. In this study, we propose methods for OPE and OPL in two-player zero-sum Markov games. For OPE, we estimate exploitability that is often used as a metric for determining how close a strategy profile is to a Nash equilibrium in two-player zero-sum games. For OPL, we calculate maximin policies as Nash equilibrium strategies over the historical data. We prove the exploitability estimation error bounds for OPE and regret bounds for OPL based on the doubly robust and double reinforcement learning estimators. Finally, we demonstrate the effectiveness and performance of the proposed methods through experiments.

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