Robust Offline Reinforcement Learning for Non-Markovian Decision Processes

• URL: http://arxiv.org/abs/2411.07514v1
• Date: Tue, 12 Nov 2024 03:22:56 GMT
• Title: Robust Offline Reinforcement Learning for Non-Markovian Decision Processes
• Authors: Ruiquan Huang, Yingbin Liang, Jing Yang,
• Abstract summary: We study the learning problem of robust offline non-Markovian RL. We introduce a novel dataset distillation and a lower confidence bound (LCB) design for robust values under different types of the uncertainty set. 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 $epsilon$-optimal robust policy.
• Score: 48.9399496805422
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• Abstract: 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 $\epsilon$-optimal robust policy using $O(1/\epsilon^2)$ 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.

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