The Impact of Data Distribution on Q-learning with Function Approximation

TL;DR

This paper investigates how the properties of data distribution affect the performance of Q-learning algorithms with function approximation, combining theoretical insights and empirical validation across different environments.

Contribution

It introduces a novel four-state MDP to analyze data distribution effects and provides a comprehensive theoretical and empirical study on offline Q-learning performance.

Findings

High entropy data distributions improve offline learning.

Data diversity and quality jointly enhance offline Q-learning.

Theoretical bounds connect data properties to algorithm performance.

Abstract

We study the interplay between the data distribution and Q-learning-based algorithms with function approximation. We provide a unified theoretical and empirical analysis as to how different properties of the data distribution influence the performance of Q-learning-based algorithms. We connect different lines of research, as well as validate and extend previous results. We start by reviewing theoretical bounds on the performance of approximate dynamic programming algorithms. We then introduce a novel four-state MDP specifically tailored to highlight the impact of the data distribution in the performance of Q-learning-based algorithms with function approximation, both online and offline. Finally, we experimentally assess the impact of the data distribution properties on the performance of two offline Q-learning-based algorithms under different environments. According to our results: (i) high entropy data distributions are well-suited for learning in an offline manner; and (ii) a certain degree of data diversity (data coverage) and data quality (closeness to optimal policy) are jointly desirable for offline learning.