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On Sample-Efficient Offline Reinforcement Learning: Data Diversity, Posterior Sampling, and Beyond

Thanh Nguyen-Tang, Raman Arora

TL;DR

The paper addresses sample-efficiency in offline reinforcement learning with function approximation by introducing a unified data-diversity framework ${\mathcal{C}}(\pi;{\epsilon_c})$ that quantifies extrapolation from behavior to target policies. It unifies three algorithmic paradigms—version-space-based, regularized optimization, and posterior sampling—under the GOPO framework, and proves that they achieve comparable sub-optimality bounds under standard assumptions, even with adaptive offline data. A novel model-free posterior sampling approach (PSC) is proposed, incorporating a pessimistic prior to enforce cautious value estimates, with frequentist guarantees. The results generalize prior coverage notions, tighten extrapolation controls, and extend applicability to finite and linear function classes, offering practical alternatives with provable performance in partially diverse offline data. Overall, the work broadens the set of sample-efficient offline RL methods and clarifies how data diversity governs offline learnability and algorithmic design.

Abstract

We seek to understand what facilitates sample-efficient learning from historical datasets for sequential decision-making, a problem that is popularly known as offline reinforcement learning (RL). Further, we are interested in algorithms that enjoy sample efficiency while leveraging (value) function approximation. In this paper, we address these fundamental questions by (i) proposing a notion of data diversity that subsumes the previous notions of coverage measures in offline RL and (ii) using this notion to {unify} three distinct classes of offline RL algorithms based on version spaces (VS), regularized optimization (RO), and posterior sampling (PS). We establish that VS-based, RO-based, and PS-based algorithms, under standard assumptions, achieve \emph{comparable} sample efficiency, which recovers the state-of-the-art sub-optimality bounds for finite and linear model classes with the standard assumptions. This result is surprising, given that the prior work suggested an unfavorable sample complexity of the RO-based algorithm compared to the VS-based algorithm, whereas posterior sampling is rarely considered in offline RL due to its explorative nature. Notably, our proposed model-free PS-based algorithm for offline RL is {novel}, with sub-optimality bounds that are {frequentist} (i.e., worst-case) in nature.

On Sample-Efficient Offline Reinforcement Learning: Data Diversity, Posterior Sampling, and Beyond

TL;DR

The paper addresses sample-efficiency in offline reinforcement learning with function approximation by introducing a unified data-diversity framework that quantifies extrapolation from behavior to target policies. It unifies three algorithmic paradigms—version-space-based, regularized optimization, and posterior sampling—under the GOPO framework, and proves that they achieve comparable sub-optimality bounds under standard assumptions, even with adaptive offline data. A novel model-free posterior sampling approach (PSC) is proposed, incorporating a pessimistic prior to enforce cautious value estimates, with frequentist guarantees. The results generalize prior coverage notions, tighten extrapolation controls, and extend applicability to finite and linear function classes, offering practical alternatives with provable performance in partially diverse offline data. Overall, the work broadens the set of sample-efficient offline RL methods and clarifies how data diversity governs offline learnability and algorithmic design.

Abstract

We seek to understand what facilitates sample-efficient learning from historical datasets for sequential decision-making, a problem that is popularly known as offline reinforcement learning (RL). Further, we are interested in algorithms that enjoy sample efficiency while leveraging (value) function approximation. In this paper, we address these fundamental questions by (i) proposing a notion of data diversity that subsumes the previous notions of coverage measures in offline RL and (ii) using this notion to {unify} three distinct classes of offline RL algorithms based on version spaces (VS), regularized optimization (RO), and posterior sampling (PS). We establish that VS-based, RO-based, and PS-based algorithms, under standard assumptions, achieve \emph{comparable} sample efficiency, which recovers the state-of-the-art sub-optimality bounds for finite and linear model classes with the standard assumptions. This result is surprising, given that the prior work suggested an unfavorable sample complexity of the RO-based algorithm compared to the VS-based algorithm, whereas posterior sampling is rarely considered in offline RL due to its explorative nature. Notably, our proposed model-free PS-based algorithm for offline RL is {novel}, with sub-optimality bounds that are {frequentist} (i.e., worst-case) in nature.
Paper Structure (62 sections, 30 theorems, 170 equations, 1 figure, 3 tables, 1 algorithm)

This paper contains 62 sections, 30 theorems, 170 equations, 1 figure, 3 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Overview of Techniques.
  3. Background and problem formulation
  4. Episodic time-inhomogenous Markov decision process
  5. Additional notation.
  6. Offline data generation
  7. Value sub-optimality.
  8. Policy and function classes
  9. Effective sizes of policy and function classes
  10. Algorithms
  11. Version space-based critic (VSC) (\ref{['algorithm: vsc']}).
  12. Regularized optimization-based critic (ROC) (\ref{['algorithm: roc']}).
  13. Posterior sampling-based critic (PSC) in \ref{['algorithm: psc']}.
  14. Main results
  15. Data diversity
  16. ...and 47 more sections

Key Result

Theorem 1

Let $\hat{\pi}^{vs}$ be the output of algorithm: generic framework invoked with CriticCompute being VSC(${\mathcal{D}}, {\mathcal{F}}, \pi^t, \beta$) (algorithm: vsc) with $\beta = {\mathcal{O}}(b^2 K {\epsilon} + b K \max_{h \in [H]} \xi_h + H b^2 \max\{\tilde{d}_{opt}({\epsilon}, T), \ln (H/\delt

Figures (1)

  • Figure 1: The relations of sample-efficient offline RL classes under different data coverage measures. Given the same MDP and a target policy (e.g., an optimal policy of the MDP), each data coverage measure induces a corresponding set of behavior policies (represented by the rectangle labelled by the data coverage measure) from which the target policy is offline-learnable.

Theorems & Definitions (65)

  • Definition 1: Adaptively collected data
  • Definition 2
  • Definition 3
  • Theorem 1: Guarantees for GOPO-VSC
  • Theorem 2: Guarantees for GOPO-ROC
  • Theorem 3: Guarantees for GOPO-PSC
  • Proposition 1: A unified guarantee for VS, RO and PS
  • Lemma A.1
  • proof : Proof of \ref{['lemma: the squared residuals bound the expected value and the variance of the empirical minimax error']}
  • Lemma A.2: Freedman's inequality
  • ...and 55 more