Robust Constrained Reinforcement Learning

Yue Wang, Fei Miao, Shaofeng Zou

Abstract: Constrained reinforcement learning is to maximize the reward subject to constraints on utilities/costs. However, in practice it is often the case that the training environment is not the same as the test one, due to, e.g., modeling error, adversarial attack, non-stationarity, resulting in severe performance degradation and more importantly constraint violation in the test environment. To address this challenge, we formulate the framework of robust constrained reinforcement learning under model uncertainty, where the MDP is not fixed but lies in some uncertainty set. The goal is two fold: 1) to guarantee that constraints on utilities/costs are satisfied for all MDPs in the uncertainty set, and 2) to maximize the worst-case reward performance over the uncertainty set. We design a robust primal-dual approach, and further develop theoretical guarantee on its convergence, complexity and robust feasibility. We then investigate a concrete example of $\delta$-contamination uncertainty set, design an online and model-free algorithm and theoretically characterize its sample complexity.

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