Information-Theoretic Considerations in Batch Reinforcement Learning (1905.00360v1)

Abstract: Value-function approximation methods that operate in batch mode have foundational importance to reinforcement learning (RL). Finite sample guarantees for these methods often crucially rely on two types of assumptions: (1) mild distribution shift, and (2) representation conditions that are stronger than realizability. However, the necessity ("why do we need them?") and the naturalness ("when do they hold?") of such assumptions have largely eluded the literature. In this paper, we revisit these assumptions and provide theoretical results towards answering the above questions, and make steps towards a deeper understanding of value-function approximation.

• The paper clarifies that a mild distribution shift is vital to guarantee polynomial sample complexity in batch RL.
• The paper demonstrates that ensuring representation beyond realizability, such as completeness, is essential for reliable value-function approximation.
• The paper shows that model-based RL can bypass stringent assumptions, delineating a clear separation from value-based methods in practice.

Information-Theoretic Considerations in Batch Reinforcement Learning

The paper "Information-Theoretic Considerations in Batch Reinforcement Learning" by Jinglin Chen and Nan Jiang offers a comprehensive examination of foundational assumptions in the context of value-function approximation in batch-mode reinforcement learning (RL). The primary focus of the paper is to scrutinize the necessity and applicability of two critical assumptions that underpin many existing analytical frameworks and to explore their implications within both theoretical and practical RL paradigms.

Key Contributions

This work revisits two pivotal assumptions necessary for robust theoretical guarantees in batch-mode RL with function approximation:

1. Mild Distribution Shift: This assumption concerns the need for data distributions that have adequate coverage over the state-action space to ensure that algorithms can derive meaningful policies. The authors argue that without this assumption, it is impossible to recover polynomial sample complexity unless constraints on the dynamics of the Markov Decision Processes (MDPs) are imposed.
2. Representation Condition Beyond Realizability: While realizability mandates that the function class contains (or approximates) the optimal value function, the authors highlight the need for assumptions like completeness that are significantly stronger. Completeness assumes that the function class is closed under the BeLLMan operator.

The authors achieve several notable results through their systematic exploration of these assumptions:

• Sample Complexity Bounds: The paper refines the sample complexity analysis of the Fitted Q-Iteration (FQI) and its minimax variants, demonstrating that the lack of a mild distribution shift or a sufficient function representation can lead to deteriorated learning performance.
• Information-Theoretic Lower Bounds: The authors employ information-theoretic arguments to underline the necessity of mild distribution shift by showing that in its absence, even favorable data distributions cannot guarantee efficient learning unless MDP dynamics are inherently restricted.
• Separation of Model-Based and Value-Based RL: It is shown that model-based RL under batch settings can achieve polynomial sample complexity without assumptions beyond realizability, whereas strong conditions beyond realizability seem inevitable for value-based RL methods.

Theoretical Implications

The insights garnered from this paper hold substantial implications for the theoretical underpinnings of RL:

• Necessity of Distributional and Representational Assumptions: The work elucidates the reasons such assumptions are not merely artifacts of theoretical analysis but fundamental requirements for achieving finite sample guarantees.
• Connections to Online Learning: There exists an interesting parallel between the definition of concentrability and notions such as BeLLMan rank, which have been instrumental in facilitating sample-efficient exploration within an online setting.
• Abstractions and Representational Power: Through an exploration of bisimulation and state abstractions, the authors provide clarity on the intricate relationship between the representational capacity of function classes and the conditions under which completeness might hold.

Practical Significance

Practically, the insights could influence the design of robust RL algorithms capable of leveraging off-policy data in batch settings commonly found in real-world applications such as healthcare and robotics:

• Realistic Data Assumptions: By refining understanding of the data coverage requirements (concentrability condition), practitioners can better design data collection strategies or assess the feasibility of RL deployments in existing information environments.
• Function Class Design: Designers of RL algorithms can pay heed to the type of function approximation utilized in algorithms, taking into account completeness and bisimulation considerations highlighted in the findings.

Future Directions

The exploration provided in this paper paves the way for future investigations that could relax some of these foundational assumptions or provide alternative frameworks. Particularly intriguing is the challenge associated with representing environments where exact bisimulation might be computationally infeasible. Here, future work might focus on efficiently approximating completeness or developing adaptive thresholding techniques for quantifying distribution shifts. Moreover, the speculation about future alignment of concentratability definitions with practical function class structures can potentially open new avenues of research in both theoretical and applied reinforcement learning.

Ultimately, the paper strongly advocates for a dialogue between theoretical insights and empirical observations to guide the evolution of RL techniques that are both theoretically sound and practically viable.