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| Format: | Preprint |
| Veröffentlicht: |
2023
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| Online-Zugang: | https://arxiv.org/abs/2305.13289 |
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| _version_ | 1866909328014835712 |
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| author | Wang, Yue Xiong, Jinjun Zou, Shaofeng |
| author_facet | Wang, Yue Xiong, Jinjun Zou, Shaofeng |
| contents | Offline reinforcement learning aims to learn from pre-collected datasets without active exploration. This problem faces significant challenges, including limited data availability and distributional shifts. Existing approaches adopt a pessimistic stance towards uncertainty by penalizing rewards of under-explored state-action pairs to estimate value functions conservatively. In this paper, we show that the distributionally robust optimization (DRO) based approach can also address these challenges and is {asymptotically minimax optimal}. Specifically, we directly model the uncertainty in the transition kernel and construct an uncertainty set of statistically plausible transition kernels. We then show that the policy that optimizes the worst-case performance over this uncertainty set has a near-optimal performance in the underlying problem. We first design a metric-based distribution-based uncertainty set such that with high probability the true transition kernel is in this set. We prove that to achieve a sub-optimality gap of $ε$, the sample complexity is $\mathcal{O}(S^2C^{π^*}ε^{-2}(1-γ)^{-4})$, where $γ$ is the discount factor, $S$ is the number of states, and $C^{π^*}$ is the single-policy clipped concentrability coefficient which quantifies the distribution shift. To achieve the optimal sample complexity, we further propose a less conservative value-function-based uncertainty set, which, however, does not necessarily include the true transition kernel. We show that an improved sample complexity of $\mathcal{O}(SC^{π^*}ε^{-2}(1-γ)^{-3})$ can be obtained, which asymptotically matches with the minimax lower bound for offline reinforcement learning, and thus is asymptotically minimax optimal. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_13289 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Achieving the Asymptotically Optimal Sample Complexity of Offline Reinforcement Learning: A DRO-Based Approach Wang, Yue Xiong, Jinjun Zou, Shaofeng Machine Learning Offline reinforcement learning aims to learn from pre-collected datasets without active exploration. This problem faces significant challenges, including limited data availability and distributional shifts. Existing approaches adopt a pessimistic stance towards uncertainty by penalizing rewards of under-explored state-action pairs to estimate value functions conservatively. In this paper, we show that the distributionally robust optimization (DRO) based approach can also address these challenges and is {asymptotically minimax optimal}. Specifically, we directly model the uncertainty in the transition kernel and construct an uncertainty set of statistically plausible transition kernels. We then show that the policy that optimizes the worst-case performance over this uncertainty set has a near-optimal performance in the underlying problem. We first design a metric-based distribution-based uncertainty set such that with high probability the true transition kernel is in this set. We prove that to achieve a sub-optimality gap of $ε$, the sample complexity is $\mathcal{O}(S^2C^{π^*}ε^{-2}(1-γ)^{-4})$, where $γ$ is the discount factor, $S$ is the number of states, and $C^{π^*}$ is the single-policy clipped concentrability coefficient which quantifies the distribution shift. To achieve the optimal sample complexity, we further propose a less conservative value-function-based uncertainty set, which, however, does not necessarily include the true transition kernel. We show that an improved sample complexity of $\mathcal{O}(SC^{π^*}ε^{-2}(1-γ)^{-3})$ can be obtained, which asymptotically matches with the minimax lower bound for offline reinforcement learning, and thus is asymptotically minimax optimal. |
| title | Achieving the Asymptotically Optimal Sample Complexity of Offline Reinforcement Learning: A DRO-Based Approach |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2305.13289 |