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arXiv · 2109.03396

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

Mehdi Jafarnia-Jahromi·Rahul Jain·Ashutosh Nayyar
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Abstract

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. Our regret bound improves on 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 $T$.

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Mehdi Jafarnia-Jahromi, Rahul Jain, Ashutosh Nayyar. 2021-09-08. A Bayesian Learning Algorithm for Unknown Zero-sum Stochastic Games with an Arbitrary Opponent. https://arxiv.org/abs/2109.03396

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