Theoretical Analysis of Offline Reinforcement Learning Under Partial Coverage and Q-Approximation
Researchers published a theoretical study on offline reinforcement learning, answering that Q-realizability and Bellman completeness alone are insufficient for sample-efficient learning under partial coverage. The work introduces a decision-estimation framework that decomposes offline RL complexity and provides improved sample complexity bounds for soft Q-learning. The findings advance understanding of practical algorithms like Conservative Q-Learning and establish new theoretical foundations for offline RL in previously unexplored settings.
A new arXiv paper addresses fundamental theoretical questions about offline reinforcement learning, specifically examining whether Q-realizability and Bellman completeness are sufficient for sample-efficient learning under partial coverage—a setting motivated by practical algorithms like Conservative Q-Learning. The authors answer this question negatively through information-theoretic lower bounds and propose a general decision-estimation framework that decomposes offline RL complexity into decision complexity and value estimation error. Their contributions include the first ε⁻² sample complexity bound for soft Q-learning under partial coverage (improving prior ε⁻⁴ bounds), removal of the need for additional online interaction in certain settings, new characterizations of Bellman completeness's role, and the first analysis of offline learnability for general low-Bellman-rank MDPs. The work also provides the first theoretical analysis of Conservative Q-Learning in the function approximation setting, unifying and extending several existing results.
What's missing
The paper does not discuss empirical validation of the theoretical bounds on real-world offline RL tasks, nor does it compare the practical performance of algorithms derived from this framework against existing methods like CQL on benchmark environments.
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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