In this paper, we propose Posterior Sampling Reinforcement Learning for Zero-sum Stochastic Games (PSRL-ZSG), the first online learning algorithm that achieves Bayesian regret bound of $O(HS\sqrt{AT})$ in the infinite-horizon zero-sum stochastic games with average-reward criterion. Here $H$ is an upper bound on the span of the bias function, $S$ is the number of states, $A$ is the number of joint actions and $T$ is the horizon. We consider the online setting where the opponent can not be controlled and can take any arbitrary time-adaptive history-dependent strategy. This improves the best existing regret bound of $O(\sqrt[3]{DS^2AT^2})$ by Wei et. al., 2017 under the same assumption and matches the theoretical lower bound in $A$ and $T$.

中文翻译：

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使用后验采样学习零和随机博弈

在本文中，我们提出了零和随机博弈的后采样强化学习（PSRL-ZSG），这是第一个在无限地平线上实现 $O(HS\sqrt{AT})$ 的贝叶斯后悔界的在线学习算法-sum 具有平均奖励标准的随机游戏。这里 $H$ 是偏置函数跨度的上限，$S$ 是状态数，$A$ 是联合动作的数量，$T$ 是视界。我们考虑对手无法控制的在线设置，并且可以采取任何任意的时间自适应历史依赖策略。这改进了 Wei 等人的 $O(\sqrt[3]{DS^2AT^2})$ 的最佳现有后悔界限。al., 2017 在相同的假设下并与 $A$ 和 $T$ 的理论下限相匹配。