An Empirical Study of Implicit Regularization in Deep Offline RL

TL;DR

This paper empirically investigates the relationship between implicit regularization, specifically effective rank collapse, and performance in deep offline reinforcement learning, revealing that the association is complex and context-dependent.

Contribution

It provides a detailed empirical analysis showing that the link between effective rank and performance is not straightforward and highlights the influence of various factors on this relationship.

Findings

Effective rank collapse is only associated with performance in restricted settings.

Three phases of learning explain the impact of implicit regularization.

Bootstrapping alone does not cause effective rank collapse.

Abstract

Deep neural networks are the most commonly used function approximators in offline reinforcement learning. Prior works have shown that neural nets trained with TD-learning and gradient descent can exhibit implicit regularization that can be characterized by under-parameterization of these networks. Specifically, the rank of the penultimate feature layer, also called \textit{effective rank}, has been observed to drastically collapse during the training. In turn, this collapse has been argued to reduce the model's ability to further adapt in later stages of learning, leading to the diminished final performance. Such an association between the effective rank and performance makes effective rank compelling for offline RL, primarily for offline policy evaluation. In this work, we conduct a careful empirical study on the relation between effective rank and performance on three offline RL datasets : bsuite, Atari, and DeepMind lab. We observe that a direct association exists only in restricted settings and disappears in the more extensive hyperparameter sweeps. Also, we empirically identify three phases of learning that explain the impact of implicit regularization on the learning dynamics and found that bootstrapping alone is insufficient to explain the collapse of the effective rank. Further, we show that several other factors could confound the relationship between effective rank and performance and conclude that studying this association under simplistic assumptions could be highly misleading.