Scalable Online Exploration via Coverability

TL;DR

This paper introduces a new exploration objective, $L_1$-Coverage, that improves online exploration in reinforcement learning by controlling complexity, enabling efficient planning, and supporting scalable algorithms in high-dimensional MDPs.

Contribution

The paper proposes $L_1$-Coverage as a novel exploration objective that generalizes previous schemes and supports efficient, scalable algorithms for reinforcement learning in complex environments.

Findings

$L_1$-Coverage effectively guides exploration in high-dimensional MDPs.

The proposed algorithms are computationally efficient for online reinforcement learning.

Empirical results show successful exploration using $L_1$-Coverage with standard policy optimization methods.

Abstract

Exploration is a major challenge in reinforcement learning, especially for high-dimensional domains that require function approximation. We propose exploration objectives -- policy optimization objectives that enable downstream maximization of any reward function -- as a conceptual framework to systematize the study of exploration. Within this framework, we introduce a new objective, $L_1$-Coverage, which generalizes previous exploration schemes and supports three fundamental desiderata: 1. Intrinsic complexity control. $L_1$-Coverage is associated with a structural parameter, $L_1$-Coverability, which reflects the intrinsic statistical difficulty of the underlying MDP, subsuming Block and Low-Rank MDPs. 2. Efficient planning. For a known MDP, optimizing $L_1$-Coverage efficiently reduces to standard policy optimization, allowing flexible integration with off-the-shelf methods such as policy gradient and Q-learning approaches. 3. Efficient exploration. $L_1$-Coverage enables the first computationally efficient model-based and model-free algorithms for online (reward-free or reward-driven) reinforcement learning in MDPs with low coverability. Empirically, we find that $L_1$-Coverage effectively drives off-the-shelf policy optimization algorithms to explore the state space.