A Bayesian Learning Algorithm for Unknown Zero-sum Stochastic Games with an Arbitrary Opponent
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2021
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| _version_ | 1866917608643624960 |
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| author | Jafarnia-Jahromi, Mehdi Jain, Rahul Nayyar, Ashutosh |
| author_facet | Jafarnia-Jahromi, Mehdi Jain, Rahul Nayyar, Ashutosh |
| contents | 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 $T$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2109_03396 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | A Bayesian Learning Algorithm for Unknown Zero-sum Stochastic Games with an Arbitrary Opponent Jafarnia-Jahromi, Mehdi Jain, Rahul Nayyar, Ashutosh Machine Learning Computer Science and Game Theory 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 $T$. |
| title | A Bayesian Learning Algorithm for Unknown Zero-sum Stochastic Games with an Arbitrary Opponent |
| topic | Machine Learning Computer Science and Game Theory |
| url | https://arxiv.org/abs/2109.03396 |