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arXiv · 2402.01900

Distributional Off-policy Evaluation with Bellman Residual Minimization

Sungee Hong·Zhengling Qi·Raymond K. W. Wong
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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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Sungee Hong, Zhengling Qi, Raymond K. W. Wong. 2025-03-12. Distributional Off-policy Evaluation with Bellman Residual Minimization. https://arxiv.org/abs/2402.01900

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