Model-Based Reinforcement Learning for Offline Zero-Sum Markov Games
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2022
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| _version_ | 1866912275192872960 |
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| author | Yan, Yuling Li, Gen Chen, Yuxin Fan, Jianqing |
| author_facet | Yan, Yuling Li, Gen Chen, Yuxin Fan, Jianqing |
| contents | This paper makes progress towards learning Nash equilibria in two-player zero-sum Markov games from offline data. Specifically, consider a $γ$-discounted infinite-horizon Markov game with $S$ states, where the max-player has $A$ actions and the min-player has $B$ actions. We propose a pessimistic model-based algorithm with Bernstein-style lower confidence bounds -- called VI-LCB-Game -- that provably finds an $\varepsilon$-approximate Nash equilibrium with a sample complexity no larger than $\frac{C_{\mathsf{clipped}}^{\star}S(A+B)}{(1-γ)^{3}\varepsilon^{2}}$ (up to some log factor). Here, $C_{\mathsf{clipped}}^{\star}$ is some unilateral clipped concentrability coefficient that reflects the coverage and distribution shift of the available data (vis-à-vis the target data), and the target accuracy $\varepsilon$ can be any value within $\big(0,\frac{1}{1-γ}\big]$. Our sample complexity bound strengthens prior art by a factor of $\min\{A,B\}$, achieving minimax optimality for the entire $\varepsilon$-range. An appealing feature of our result lies in algorithmic simplicity, which reveals the unnecessity of variance reduction and sample splitting in achieving sample optimality. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2206_04044 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Model-Based Reinforcement Learning for Offline Zero-Sum Markov Games Yan, Yuling Li, Gen Chen, Yuxin Fan, Jianqing Machine Learning Computer Science and Game Theory Information Theory Statistics Theory This paper makes progress towards learning Nash equilibria in two-player zero-sum Markov games from offline data. Specifically, consider a $γ$-discounted infinite-horizon Markov game with $S$ states, where the max-player has $A$ actions and the min-player has $B$ actions. We propose a pessimistic model-based algorithm with Bernstein-style lower confidence bounds -- called VI-LCB-Game -- that provably finds an $\varepsilon$-approximate Nash equilibrium with a sample complexity no larger than $\frac{C_{\mathsf{clipped}}^{\star}S(A+B)}{(1-γ)^{3}\varepsilon^{2}}$ (up to some log factor). Here, $C_{\mathsf{clipped}}^{\star}$ is some unilateral clipped concentrability coefficient that reflects the coverage and distribution shift of the available data (vis-à-vis the target data), and the target accuracy $\varepsilon$ can be any value within $\big(0,\frac{1}{1-γ}\big]$. Our sample complexity bound strengthens prior art by a factor of $\min\{A,B\}$, achieving minimax optimality for the entire $\varepsilon$-range. An appealing feature of our result lies in algorithmic simplicity, which reveals the unnecessity of variance reduction and sample splitting in achieving sample optimality. |
| title | Model-Based Reinforcement Learning for Offline Zero-Sum Markov Games |
| topic | Machine Learning Computer Science and Game Theory Information Theory Statistics Theory |
| url | https://arxiv.org/abs/2206.04044 |