In online reinforcement learning (RL), instead of employing standard structural assumptions on Markov decision processes (MDPs), using a certain coverage condition (original from offline RL) is enough to ensure sample-efficient guarantees (Xie et al. 2023). In this work, we focus on this new direction by digging more possible and general coverage conditions, and study the potential and the utility of them in efficient online RL. We identify more concepts, including the $L^p$ variant of concentrability, the density ratio realizability, and trade-off on the partial/rest coverage condition, that can be also beneficial to sample-efficient online RL, achieving improved regret bound. Furthermore, if exploratory offline data are used, under our coverage conditions, both statistically and computationally efficient guarantees can be achieved for online RL. Besides, even though the MDP structure is given, e.g., linear MDP, we elucidate that, good coverage conditions are still beneficial to obtain faster regret bound beyond $\widetilde{O}(\sqrt{T})$ and even a logarithmic order regret. These results provide a good justification for the usage of general coverage conditions in efficient online RL.

本研究聚焦于在线强化学习中，使用一定的覆盖条件能够确保样本高效，通过挖掘更多的覆盖条件，研究了其在提高样本效率方面的潜力和效用，进一步证明使用覆盖条件能够实现在线强化学习的高效性，包括 $L^p$ 集中性方差实现、密度比实现、偏差/休息覆盖条件的权衡以及基于探索性离线数据使用统计和计算有效保证等。

在线强化学习中一般覆盖条件在有效函数逼近中的可证明优势