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This research advances distributional reinforcement learning by establishing functional central limit theorems and enabling efficient online statistical inference without storing full trajectory data. The method reduces memory overhead while maintaining asymptotic validity, offering a practical tool for analyzing convergence in complex RL environments where generative models are available. It represents a significant theoretical step toward robust uncertainty quantification within deep reinforcement learning frameworks.
Online Inference for Quantile Temporal Difference Learning in Distributional Reinforcement Learning
arXiv:2608.12973v2 Announce Type: replace-cross Abstract: In this paper, we study how to perform statistical inference for quantile temporal difference learning (QTD) in distributional reinforcement learning. Assuming access to a generative model, we first establish functional central limit theorems for both synchronous and asynchronous QTD, which show that the averaged iterates of QTD converge weakly to a rescaled Brownian motion. We next provide online inference methods. Based on random scaling, the inference procedure constructs an asymptotically pivotal statistic for inference by using the information along the whole QTD path. Meanwhile, the proposed statistic can be computed online without storing the entire trajectory of QTD iterates. This substantially reduces the memory requirement and enables efficient statistical inference in distributional reinforcement learning.
Abstract:In this paper, we study how to perform statistical inference for quantile temporal difference learning (QTD) in distributional reinforcement learning. Assuming access to a generative model, we first establish functional central limit theorems for both synchronous and asynchronous QTD, which show that the averaged iterates of QTD converge weakly to a rescaled Brownian motion. We next provide online inference methods. Based on random scaling, the inference procedure constructs an asymptotically pivotal statistic for inference by using the information along the whole QTD path. Meanwhile, the proposed statistic can be computed online without storing the entire trajectory of QTD iterates. This substantially reduces the memory requirement and enables efficient statistical inference in distributional reinforcement learning.
Machine Learning (stat.ML); Machine Learning (cs.LG)
arXiv:2608.12973 [stat.ML]
(or arXiv:2608.12973v2 [stat.ML] for this version)
https://doi.org/10.48550/arXiv.2608.12973 Focus to learn more arXiv-issued DOI via DataCite
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