Distributional Off-policy Evaluation with Bellman Residual Minimization

• URL: http://arxiv.org/abs/2402.01900v2
• Date: Thu, 17 Oct 2024 03:26:07 GMT
• Title: Distributional Off-policy Evaluation with Bellman Residual Minimization
• Authors: Sungee Hong, Zhengling Qi, Raymond K. W. Wong,
• Abstract summary: We study distributional off-policy evaluation (OPE) The goal is to learn the distribution of the return for a target policy using offline data generated by a different policy. We propose a new method called Energy Bellman Residual Minimizer (EBRM)
• Score: 12.343981093497332
• License:
• Abstract: We study distributional off-policy evaluation (OPE), of which the goal is to learn the distribution of the return for a target policy using offline data generated by a different policy. The theoretical foundation of many existing work relies on the supremum-extended statistical distances such as supremum-Wasserstein distance, which are hard to estimate. In contrast, we study the more manageable expectation-extended statistical distances and provide a novel theoretical justification on their validity for learning the return distribution. Based on this attractive property, we propose a new method called Energy Bellman Residual Minimizer (EBRM) for distributional OPE. We provide corresponding in-depth theoretical analyses. We establish a finite-sample error bound for the EBRM estimator under the realizability assumption. Furthermore, we introduce a variant of our method based on a multi-step extension which improves the error bound for non-realizable settings. Notably, unlike prior distributional OPE methods, the theoretical guarantees of our method do not require the completeness assumption.

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