Search papers, labs, and topics across Lattice.
This paper investigates the sample complexity of offline reinforcement learning under $Q^\star$-approximation and partial coverage, demonstrating a negative result regarding the sufficiency of $Q^\star$-realizability and Bellman completeness. It introduces a decision-estimation decomposition framework to characterize the intrinsic complexity of $Q^\star$ function classes, improving upon existing guarantees and extending to broader settings. Furthermore, the paper establishes an $\epsilon^{-2}$ sample complexity for soft $Q$-learning under partial coverage and provides the first analysis for CQL under $Q^\star$-realizability and Bellman completeness beyond the tabular case.
Even with perfect knowledge of the optimal Q-function, learning in offline RL with partial coverage can be surprisingly hard, but a new framework based on decision-estimation coefficients (DEC) offers a path to tighter bounds and modular algorithm design.
We study offline reinforcement learning under $Q^\star$-approximation and partial coverage, a setting that motivates practical algorithms such as Conservative $Q$-Learning (CQL; Kumar et al., 2020) but has received limited theoretical attention. Our work is inspired by the following open question:"Are $Q^\star$-realizability and Bellman completeness sufficient for sample-efficient offline RL under partial coverage?"We answer in the negative by establishing an information-theoretic lower bound. Going substantially beyond this, we introduce a general framework that characterizes the intrinsic complexity of a given $Q^\star$ function class, inspired by model-free decision-estimation coefficients (DEC) for online RL (Foster et al., 2023b; Liu et al., 2025b). This complexity recovers and improves the quantities underlying the guarantees of Chen and Jiang (2022) and Uehara et al. (2023), and extends to broader settings. Our decision-estimation decomposition can be combined with a wide range of $Q^\star$ estimation procedures, modularizing and generalizing existing approaches. Beyond the general framework, we make further contributions: By developing a novel second-order performance difference lemma, we obtain the first $\epsilon^{-2}$ sample complexity under partial coverage for soft $Q$-learning, improving the $\epsilon^{-4}$ bound of Uehara et al. (2023). We remove Chen and Jiang's (2022) need for additional online interaction when the value gap of $Q^\star$ is unknown. We also give the first characterization of offline learnability for general low-Bellman-rank MDPs without Bellman completeness (Jiang et al., 2017; Du et al., 2021; Jin et al., 2021), a canonical setting in online RL that remains unexplored in offline RL except for special cases. Finally, we provide the first analysis for CQL under $Q^\star$-realizability and Bellman completeness beyond the tabular case.
