Theoretical Analysis of Offline Reinforcement Learning Under Partial Coverage and Q-Approximation
Researchers have answered a key open question in offline reinforcement learning (RL) theory, proving that Q*-realizability and Bellman completeness alone are not sufficient for sample-efficient learning under partial coverage. The work introduces a decision-estimation framework that decomposes offline RL complexity into two modular sub-problems, unifying and improving upon prior results. The findings provide stronger theoretical foundations for practical algorithms like Conservative Q-Learning and open new directions for understanding learnability in complex RL settings.
A new preprint posted to arXiv addresses a longstanding open question in offline reinforcement learning theory: whether Q*-realizability and Bellman completeness are sufficient conditions for sample-efficient offline RL under partial coverage. The authors answer definitively in the negative, establishing an information-theoretic lower bound that rules out this possibility. To characterize what additional structure is needed, they introduce a general decision-estimation framework inspired by model-free decision-estimation coefficients developed for online RL, decomposing offline RL complexity into a decision complexity component and a value estimation error component. Key improvements over prior work include the first ε⁻² sample complexity bound for soft Q-learning under partial coverage—improving a previous ε⁻⁴ bound—and the removal of the requirement for additional online interaction in certain value-gap settings. The paper also provides the first characterization of offline learnability for general low-Bellman-rank Markov decision processes, a canonical online RL setting previously unexplored in the offline context, and offers the first theoretical analysis of Conservative Q-Learning under function approximation.
What's missing
The paper is a preprint and has not yet undergone formal peer review. The authors note that the framework is primarily theoretical; empirical validation of the improved sample complexity bounds on benchmark tasks is not provided.
What different sources said
- arXiv cs.AICenter
On the Complexity of Offline Reinforcement Learning with $Q^\star$-Approximation and Partial Coverage
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