Asymptotic Analysis of Sample-averaged Q-learning
This work provides a theoretical foundation for statistical inference in reinforcement learning, which is incremental but addresses uncertainty management for RL practitioners.
The paper tackles the problem of uncertainty in reinforcement learning by introducing sample-averaged Q-learning, a framework that aggregates samples to improve statistical inference, and demonstrates through experiments that it enables effective confidence interval construction and batch scheduling strategies.
Reinforcement learning (RL) has emerged as a key approach for training agents in complex and uncertain environments. Incorporating statistical inference in RL algorithms is essential for understanding and managing uncertainty in model performance. This paper introduces a generalized framework for time-varying batch-averaged Q-learning, termed sample-averaged Q-learning (SA-QL), which extends traditional single-sample Q-learning by aggregating samples of rewards and next states to better account for data variability and uncertainty. We leverage the functional central limit theorem (FCLT) to establish a novel framework that provides insights into the asymptotic normality of the sample-averaged algorithm under mild conditions. Additionally, we develop a random scaling method for interval estimation, enabling the construction of confidence intervals without requiring extra hyperparameters. Extensive numerical experiments across classic stochastic OpenAI Gym environments, including windy gridworld and slippery frozenlake, demonstrate how different batch scheduling strategies affect learning efficiency, coverage rates, and confidence interval widths. This work establishes a unified theoretical foundation for sample-averaged Q-learning, providing insights into effective batch scheduling and statistical inference for RL algorithms.