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

TL;DR

This paper introduces PSRL-ZSG, a Bayesian learning algorithm for zero-sum stochastic games that achieves near-optimal regret bounds even against arbitrary opponents, advancing online learning in complex game settings.

Contribution

The paper presents the first online algorithm with Bayesian regret bounds for zero-sum stochastic games against arbitrary opponents, improving previous bounds significantly.

Findings

Achieves Bayesian regret of O(HS√AT) in infinite-horizon games

Outperforms previous regret bounds by Wei et al. (2017)

Matches the theoretical lower bound in T

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 $T$.