The impact of data distribution on Q-learning with function approximation

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, being primarily focused on offline settings. First, we analyze the impact of the data distribution by using optimization as a tool to better understand which data distributions yield low concentrability coefficients. We motivate high-entropy distributions from a game-theoretical point of view and propose an algorithm to find the optimal data distribution from the point of view of concentrability. Second, from an empirical perspective, we 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. Finally, we experimentally assess the impact of the data distribution properties on the performance of two offline Q-learning-based algorithms under different environments. Our results attest to the importance of different properties of the data distribution such as entropy, coverage, and data quality (closeness to optimal policy).