Sample Complexity of Robust Reinforcement Learning with a Generative Model

• URL: http://arxiv.org/abs/2112.01506v2
• Date: Fri, 3 Dec 2021 03:43:59 GMT
• Title: Sample Complexity of Robust Reinforcement Learning with a Generative Model
• Authors: Kishan Panaganti and Dileep Kalathil
• Abstract summary: We propose a model-based reinforcement learning (RL) algorithm for learning an $epsilon$-optimal robust policy. We consider three different forms of uncertainty sets, characterized by the total variation distance, chi-square divergence, and KL divergence. In addition to the sample complexity results, we also present a formal analytical argument on the benefit of using robust policies.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-sa/4.0/
• Abstract: The Robust Markov Decision Process (RMDP) framework focuses on designing control policies that are robust against the parameter uncertainties due to the mismatches between the simulator model and real-world settings. An RMDP problem is typically formulated as a max-min problem, where the objective is to find the policy that maximizes the value function for the worst possible model that lies in an uncertainty set around a nominal model. The standard robust dynamic programming approach requires the knowledge of the nominal model for computing the optimal robust policy. In this work, we propose a model-based reinforcement learning (RL) algorithm for learning an $\epsilon$-optimal robust policy when the nominal model is unknown. We consider three different forms of uncertainty sets, characterized by the total variation distance, chi-square divergence, and KL divergence. For each of these uncertainty sets, we give a precise characterization of the sample complexity of our proposed algorithm. In addition to the sample complexity results, we also present a formal analytical argument on the benefit of using robust policies. Finally, we demonstrate the performance of our algorithm on two benchmark problems.

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