A Bayesian Learning Algorithm for Unknown Zero-sum Stochastic Games with an Arbitrary Opponent
Mehdi Jafarnia Jahromi, Rahul A Jain, Ashutosh Nayyar
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 $\tilde\mathcal{O}(HS\sqrt{AT})$ 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 $\tilde\mathcal{O}(\sqrt[3]{DS^2AT^2})$ by Wei et al., (2017) under the same assumption and matches the theoretical lower bound in $T$.
BibTeX
@InProceedings{pmlr-v238-jafarnia-jahromi24a,
title = {A {B}ayesian Learning Algorithm for Unknown Zero-sum Stochastic Games with an Arbitrary Opponent},
author = {Jafarnia Jahromi, Mehdi and A Jain, Rahul and Nayyar, Ashutosh},
booktitle = {Proceedings of The 27th International Conference on Artificial Intelligence and Statistics},
pages = {3880--3888},
year = {2024},
editor = {Dasgupta, Sanjoy and Mandt, Stephan and Li, Yingzhen},
volume = {238},
series = {Proceedings of Machine Learning Research},
month = {02--04 May},
publisher = {PMLR},
pdf = {https://proceedings.mlr.press/v238/jafarnia-jahromi24a/jafarnia-jahromi24a.pdf},
url = {https://proceedings.mlr.press/v238/jafarnia-jahromi24a.html},
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 $\tilde\mathcal{O}(HS\sqrt{AT})$ 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 $\tilde\mathcal{O}(\sqrt[3]{DS^2AT^2})$ by Wei et al., (2017) under the same assumption and matches the theoretical lower bound in $T$.}
}