The Role of Coverage in Online Reinforcement Learning

TL;DR

This paper reveals that good coverage conditions, especially coverability, are crucial for enabling sample-efficient online reinforcement learning, linking offline data properties to online exploration success.

Contribution

It establishes a novel connection between coverage conditions and online RL sample efficiency, introducing the sequential extrapolation coefficient as a new complexity measure.

Findings

Coverability enables sample-efficient online RL even without prior knowledge of the data distribution.

Weaker coverage notions are insufficient for online RL, despite their sufficiency for offline RL.

Existing complexity measures like Bellman rank do not fully capture coverability, leading to the proposal of a new measure.

Abstract

Coverage conditions -- which assert that the data logging distribution adequately covers the state space -- play a fundamental role in determining the sample complexity of offline reinforcement learning. While such conditions might seem irrelevant to online reinforcement learning at first glance, we establish a new connection by showing -- somewhat surprisingly -- that the mere existence of a data distribution with good coverage can enable sample-efficient online RL. Concretely, we show that coverability -- that is, existence of a data distribution that satisfies a ubiquitous coverage condition called concentrability -- can be viewed as a structural property of the underlying MDP, and can be exploited by standard algorithms for sample-efficient exploration, even when the agent does not know said distribution. We complement this result by proving that several weaker notions of coverage, despite being sufficient for offline RL, are insufficient for online RL. We also show that existing complexity measures for online RL, including Bellman rank and Bellman-Eluder dimension, fail to optimally capture coverability, and propose a new complexity measure, the sequential extrapolation coefficient, to provide a unification.