Sample Complexity of Variance-reduced Distributionally Robust Q-learning

• URL: http://arxiv.org/abs/2305.18420v2
• Date: Wed, 4 Sep 2024 05:03:06 GMT
• Title: Sample Complexity of Variance-reduced Distributionally Robust Q-learning
• Authors: Shengbo Wang, Nian Si, Jose Blanchet, Zhengyuan Zhou,
• Abstract summary: This paper presents two novel model-free algorithms, namely the distributionally robust Q-learning and its variance-reduced counterpart, that can effectively learn a robust policy despite distributional shifts. A series of numerical experiments confirm the theoretical findings and the efficiency of the algorithms in handling distributional shifts.
• Score: 17.96094201655567
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Dynamic decision-making under distributional shifts is of fundamental interest in theory and applications of reinforcement learning: The distribution of the environment in which the data is collected can differ from that of the environment in which the model is deployed. This paper presents two novel model-free algorithms, namely the distributionally robust Q-learning and its variance-reduced counterpart, that can effectively learn a robust policy despite distributional shifts. These algorithms are designed to efficiently approximate the $q$-function of an infinite-horizon $\gamma$-discounted robust Markov decision process with Kullback-Leibler ambiguity set to an entry-wise $\epsilon$-degree of precision. Further, the variance-reduced distributionally robust Q-learning combines the synchronous Q-learning with variance-reduction techniques to enhance its performance. Consequently, we establish that it attains a minimax sample complexity upper bound of $\tilde O(|\mathbf{S}||\mathbf{A}|(1-\gamma)^{-4}\epsilon^{-2})$, where $\mathbf{S}$ and $\mathbf{A}$ denote the state and action spaces. This is the first complexity result that is independent of the ambiguity size $\delta$, thereby providing new complexity theoretic insights. Additionally, a series of numerical experiments confirm the theoretical findings and the efficiency of the algorithms in handling distributional shifts.

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