Bellman-consistent Pessimism for Offline Reinforcement Learning

Abstract: The use of pessimism, when reasoning about datasets lacking exhaustive exploration has recently gained prominence in offline reinforcement learning. Despite the robustness it adds to the algorithm, overly pessimistic reasoning can be equally damaging in precluding the discovery of good policies, which is an issue for the popular bonus-based pessimism. In this paper, we introduce the notion of Bellman-consistent pessimism for general function approximation: instead of calculating a point-wise lower bound for the value function, we implement pessimism at the initial state over the set of functions consistent with the Bellman equations. Our theoretical guarantees only require Bellman closedness as standard in the exploratory setting, in which case bonus-based pessimism fails to provide guarantees. Even in the special case of linear function approximation where stronger expressivity assumptions hold, our result improves upon a recent bonus-based approach by $\mathcal{O}(d)$ in its sample complexity when the action space is finite. Remarkably, our algorithms automatically adapt to the best bias-variance tradeoff in the hindsight, whereas most prior approaches require tuning extra hyperparameters a priori.

• The paper introduces a Bellman-consistent pessimism approach that limits pessimism to the initial state, addressing inefficiencies of bonus-based methods in offline RL.
• It presents theoretical guarantees with improved sample complexity (O(d)) and an adaptive bias-variance tradeoff for linear function approximation.
• The study offers a computationally efficient variant using Lagrangian relaxation, widening offline RL applicability in scenarios with limited exploratory data.

An Analysis of Bellman-consistent Pessimism in Offline Reinforcement Learning

In the research paper titled "Bellman-consistent Pessimism for Offline Reinforcement Learning," the authors introduce a novel approach to offline reinforcement learning (RL) that hinges on Bellman-consistent pessimism. The core contribution of the paper lies in the enhancement of offline RL algorithms by integrating a pessimistic approach aligned with the Bellman equations. This contrasts sharply with traditional bonus-based pessimism methods that often result in overly conservative bias, thereby impeding the discovery of optimal policies when exploration is insufficient.

The paper articulates an algorithmic framework that leverages past dataset experiences to inform policy decisions in offline environments. The authors challenge the prevalent bonus-based pessimism techniques by proposing Bellman-consistent pessimism. This approach restricts pessimism calculation to the initial state, ensuring consistency across the entire set of functions satisfying Bellman equations, rather than applying an arbitrary point-wise lower bound.

Theoretical Contributions

Key theoretical contributions include guarantees that require only Bellman closedness, diverging from the bonus-based pessimism techniques which fail under such exploratory data insufficiency. The authors propose optimistic sample complexity results for linear function approximation, exemplified by an improvement of $\mathcal{O}(d)$ in sample efficiency under conditions with finite action spaces, contrasting with standard bonus-based methods.

The theoretical framework employs an information-theoretic algorithm poised to automatically adapt to the best bias-variance tradeoff retrospectively. This adaptive quality is crucial, allowing the algorithm to function efficiently without needing predefined hyperparameter tuning, thus eliminating an inherent shortcoming of previous methodologies.

Empirical and Practical Implications

In practical terms, the research introduces a computationally feasible variant of the proposed algorithm, leveraging a Lagrangian relaxation technique combined with recent advances in soft policy iteration. This implementation enables a computationally efficient trajectory through iterative updates capable of querying a regularized loss minimization oracle, with a slight trade-off in tighter theoretical assurances.

The study expands significantly on the existing literature by addressing cases with less than full coverage in the dataset. It's notable in the way it allows practitioners to ensure policy improvement without making stringent assumptions about the availability of exploratory data and presents substantial implications for fields where data collection is costly or risky, such as autonomous vehicles or medical decision-making systems.

Prospective Developments

The adoption of Bellman-consistent pessimism represents a meaningful advance in offline RL theory and application, setting a precedent for further exploration in leveraging function approximation classes beyond linear settings. Future work will likely explore the refinement of the adaptive mechanisms within the proposed algorithms, potentially incorporating deep representation learning techniques to further generalize across state spaces.

This paper is a marked stride toward robust and efficient offline reinforcement learning, departing from the necessity of harsh assumptions and imprecise pessimistic bounds. The adoption of such approaches can open new avenues in environments where direct interaction is constrained or undesirable, significantly enhancing the applicability of RL solutions across numerous real-world scenarios.