Robust Offline Reinforcement Learning for Non-Markovian Decision Processes
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arXiv
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| Format: | Preprint |
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2024
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| author | Huang, Ruiquan Liang, Yingbin Yang, Jing |
| author_facet | Huang, Ruiquan Liang, Yingbin Yang, Jing |
| contents | Distributionally robust offline reinforcement learning (RL) aims to find a policy that performs the best under the worst environment within an uncertainty set using an offline dataset collected from a nominal model. While recent advances in robust RL focus on Markov decision processes (MDPs), robust non-Markovian RL is limited to planning problem where the transitions in the uncertainty set are known. In this paper, we study the learning problem of robust offline non-Markovian RL. Specifically, when the nominal model admits a low-rank structure, we propose a new algorithm, featuring a novel dataset distillation and a lower confidence bound (LCB) design for robust values under different types of the uncertainty set. We also derive new dual forms for these robust values in non-Markovian RL, making our algorithm more amenable to practical implementation. By further introducing a novel type-I concentrability coefficient tailored for offline low-rank non-Markovian decision processes, we prove that our algorithm can find an $ε$-optimal robust policy using $O(1/ε^2)$ offline samples. Moreover, we extend our algorithm to the case when the nominal model does not have specific structure. With a new type-II concentrability coefficient, the extended algorithm also enjoys polynomial sample efficiency under all different types of the uncertainty set. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_07514 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Robust Offline Reinforcement Learning for Non-Markovian Decision Processes Huang, Ruiquan Liang, Yingbin Yang, Jing Machine Learning Distributionally robust offline reinforcement learning (RL) aims to find a policy that performs the best under the worst environment within an uncertainty set using an offline dataset collected from a nominal model. While recent advances in robust RL focus on Markov decision processes (MDPs), robust non-Markovian RL is limited to planning problem where the transitions in the uncertainty set are known. In this paper, we study the learning problem of robust offline non-Markovian RL. Specifically, when the nominal model admits a low-rank structure, we propose a new algorithm, featuring a novel dataset distillation and a lower confidence bound (LCB) design for robust values under different types of the uncertainty set. We also derive new dual forms for these robust values in non-Markovian RL, making our algorithm more amenable to practical implementation. By further introducing a novel type-I concentrability coefficient tailored for offline low-rank non-Markovian decision processes, we prove that our algorithm can find an $ε$-optimal robust policy using $O(1/ε^2)$ offline samples. Moreover, we extend our algorithm to the case when the nominal model does not have specific structure. With a new type-II concentrability coefficient, the extended algorithm also enjoys polynomial sample efficiency under all different types of the uncertainty set. |
| title | Robust Offline Reinforcement Learning for Non-Markovian Decision Processes |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2411.07514 |