Model-Free Robust Reinforcement Learning with Sample Complexity Analysis

• URL: http://arxiv.org/abs/2406.17096v1
• Date: Mon, 24 Jun 2024 19:35:26 GMT
• Title: Model-Free Robust Reinforcement Learning with Sample Complexity Analysis
• Authors: Yudan Wang, Shaofeng Zou, Yue Wang,
• Abstract summary: This paper proposes a model-free DR-RL algorithm leveraging the Multi-level Monte Carlo technique. We develop algorithms for uncertainty sets defined by total variation, Chi-square divergence, and KL divergence. Remarkably, our algorithms represent the first model-free DR-RL approach featuring finite sample complexity.
• Score: 16.477827600825428
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Distributionally Robust Reinforcement Learning (DR-RL) aims to derive a policy optimizing the worst-case performance within a predefined uncertainty set. Despite extensive research, previous DR-RL algorithms have predominantly favored model-based approaches, with limited availability of model-free methods offering convergence guarantees or sample complexities. This paper proposes a model-free DR-RL algorithm leveraging the Multi-level Monte Carlo (MLMC) technique to close such a gap. Our innovative approach integrates a threshold mechanism that ensures finite sample requirements for algorithmic implementation, a significant improvement than previous model-free algorithms. We develop algorithms for uncertainty sets defined by total variation, Chi-square divergence, and KL divergence, and provide finite sample analyses under all three cases. Remarkably, our algorithms represent the first model-free DR-RL approach featuring finite sample complexity for total variation and Chi-square divergence uncertainty sets, while also offering an improved sample complexity and broader applicability compared to existing model-free DR-RL algorithms for the KL divergence model. The complexities of our method establish the tightest results for all three uncertainty models in model-free DR-RL, underscoring the effectiveness and efficiency of our algorithm, and highlighting its potential for practical applications.

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