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In this paper, we propose Posterior Sampling Reinforcement Learning forZero-sum Stochastic Games (PSRL-ZSG), the first online learning algorithm thatachieves Bayesian regret bound of $O(HS\sqrt{AT})$ in the infinite-horizonzero-sum stochastic games with average-reward criterion. Here $H$ is an upperbound on the span of the bias function, $S$ is the number of states, $A$ is thenumber of joint actions and $T$ is the horizon. We consider the online settingwhere the opponent can not be controlled and can take any arbitrarytime-adaptive history-dependent strategy. Our regret bound improves on the bestexisting regret bound of $O(\sqrt[3]{DS^2AT^2})$ by Wei et al. (2017) under thesame assumption and matches the theoretical lower bound in $T$.

A Bayesian Learning Algorithm for Unknown Zero-sum Stochastic Games with an Arbitrary Opponent