The Role of Coverage in Online Reinforcement Learning (2210.04157v1)

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.

• The paper introduces the coverability coefficient, demonstrating that favorable data distribution can drive sample-efficient online RL exploration.
• It shows that weaker offline coverage notions like single-policy concentrability fail to ensure efficiency in online reinforcement learning.
• The authors propose the sequential extrapolation coefficient to capture structural conditions that existing complexity measures do not address.

Analyzing "The Role of Coverage in Online Reinforcement Learning"

The paper "The Role of Coverage in Online Reinforcement Learning" investigates the significance of coverage conditions and their impact on the sample complexity in online reinforcement learning (RL). Specifically, it explores the notion of coverability in Markov Decision Processes (MDPs) and establishes its sufficiency for efficient online RL.

Key Contributions and Results:

The authors present a new structural parameter termed the "coverability coefficient" to describe the potential for efficient exploration in online reinforcement learning. Coverability quantifies the existence of a data distribution that satisfies a prevalent offline RL coverage condition, known as concentrability.

1. Sample-Efficient Exploration via Coverability:
   • The paper demonstrates that the mere existence of a favorable data distribution can facilitate sample-efficient exploration in online RL, even without explicit knowledge of this distribution.
   • It establishes that standard RL algorithms can exploit coverability for efficient exploration, provided the underlying MDP meets standard completeness conditions.
2. Failure of Weaker Notions:
   • The authors compare coverability with weaker coverage conditions that suffice for offline settings, such as single-policy concentrability and BeLLMan residual coverage. These weaker conditions are shown to be inadequate for online RL, underscoring that offline coverage cannot necessarily translate directly into online exploration capabilities.
3. Limitation of Existing Complexity Measures:
   • Conventional complexity measures, including BeLLMan-Eluder dimension and BeLLMan rank, do not capture the concept of coverability effectively. These measures are insufficient to describe the potential for sample-efficient online RL.
4. Sequential Extrapolation Coefficient:
   • To address the inadequacy of standard complexity measures, the authors propose the "sequential extrapolation coefficient" as a new metric that aligns with the notion of coverability. It effectively unifies the various structural connections needed for efficient RL exploration.

Implications and Future Directions:

The research depicted in this paper implies significant connections between offline coverage conditions and online exploration requirements. Considering practical implementation, the concept of coverability might guide the design of exploration strategies that leverage structural properties of MDPs, reducing sample complexity and enhancing algorithmic efficiency.

Furthermore, the paper lays a foundation for exploring the interplay between offline data availability and online learning efficiency. This could be essential for developing hybrid RL approaches applicable in real-world scenarios where both historical data and active learning opportunities exist.

A curious direction for future work would be extending the results to more generalized or less restrictive completeness conditions. Additionally, investigating whether other structural properties can mirror the function that coverability provides could open new pathways for the development of practical and versatile RL algorithms. This work sets the stage for more nuanced relationships linking coverage in offline learning with exploratory efficiency in online RL environments, paving the way for more refined theories and applications in reinforcement learning.