Hybrid Reinforcement Learning Breaks Sample Size Barriers in Linear MDPs

Hybrid Reinforcement Learning (RL), where an agent learns from both an offline dataset and online explorations in an unknown environment, has garnered significant recent interest. A crucial question posed by Xie et al. (2022b) is whether hybrid RL can improve upon the existing lower bounds established for purely offline or online RL without requiring that the behavior policy visit every state and action the optimal policy does. While Li et al. (2023b) provided an affirmative answer for tabular PAC RL, the question remains unsettled for both the regretminimizing and non-tabular cases. In this work, building upon recent advancements in offline RL and reward-agnostic exploration, we develop computationally efficient algorithms for both PAC and regret-minimizing RL with linear function approximation, without requiring concentrability on the entire state-action space. We demonstrate that these algorithms achieve sharper error or regret bounds that are no worse than, and can improve on, the optimal sample complexity in offline RL (the first algorithm, for PAC RL) and online RL (the second algorithm, for regret-minimizing RL) in linear Markov decision processes (MDPs), regardless of the quality of the behavior policy. To our knowledge, this work establishes the tightest theoretical guarantees currently available for hybrid RL in linear MDPs.