Online Statistical Inference of Constant Sample-averaged Q-Learning

arXiv stat.ML / 3/31/2026

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Key Points

The paper presents a framework for performing statistical online inference for sample-averaged Q-learning, aiming to address performance instability caused by high variance and noisy or sparse rewards.
It adapts the functional central limit theorem (FCLT) to the modified sample-averaged Q-learning algorithm under general conditions to enable theoretical guarantees.
The authors construct confidence intervals for estimated Q-values using a random scaling technique derived from the inference framework.
Experiments compare the modified approach against traditional Q-learning, reporting confidence interval coverage rates and widths on a grid-world toy task and a dynamic resource-matching problem.

Abstract

Reinforcement learning algorithms have been widely used for decision-making tasks in various domains. However, the performance of these algorithms can be impacted by high variance and instability, particularly in environments with noise or sparse rewards. In this paper, we propose a framework to perform statistical online inference for a sample-averaged Q-learning approach. We adapt the functional central limit theorem (FCLT) for the modified algorithm under some general conditions and then construct confidence intervals for the Q-values via random scaling. We conduct experiments to perform inference on both the modified approach and its traditional counterpart, Q-learning using random scaling and report their coverage rates and confidence interval widths on two problems: a grid world problem as a simple toy example and a dynamic resource-matching problem as a real-world example for comparison between the two solution approaches.