A Bayesian Learning Algorithm for Unknown Zero-sum Stochastic Games with an Arbitrary Opponent
This provides a foundational algorithm for reinforcement learning in adversarial game settings, with broad implications for AI and game theory.
The paper tackles the problem of online learning in infinite-horizon zero-sum stochastic games with an arbitrary opponent, proposing PSRL-ZSG, which achieves a Bayesian regret bound of O(HS√(AT)), improving on prior work and matching the theoretical lower bound in T.
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 $T$.