We study offline-online reinforcement learning in linear mixture Markov decision processes (MDPs) under environment shift. In the offline phase, data are collected by an unknown behavior policy and may come from a mismatched environment, while in the online phase the learner interacts with the target environment. We propose an algorithm that adaptively leverages offline data. When the offline data are informative, either due to sufficient coverage or small environment shift, the algorithm provably improves over purely online learning. When the offline data are uninformative, it safely ignores them and matches the online-only performance. We establish regret upper bounds that explicitly characterize when offline data are beneficial, together with nearly matching lower bounds. Numerical experiments further corroborate our theoretical findings.

Bayesian optimization usually assumes that a Bayesian prior is given. However, the strong theoretical guarantees in Bayesian optimization are often regrettably compromised in practice because of unknown parameters in the prior. In this paper, we adopt a variant of empirical Bayes and show that, by estimating the Gaussian process prior from offline data sampled from the same prior and constructing unbiased estimators of the posterior, variants of both GP-UCB and \emph{probability of improvement} achieve a near-zero regret bound, which decreases to a constant proportional to the observational noise as the number of offline data and the number of online evaluations increase. Empirically, we have verified our approach on challenging simulated robotic problems featuring task and motion planning.

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 of-fline 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 P AC RL, the question remains unsettled for both the regret-minimizing 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 P AC 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 P AC 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.

However, existing offline RL methods tend to behave poorly during fine-tuning. In this paper, we study the fine-tuning problem in the context of conservative offline RL methods and we devise an approach for learning an effective initialization from offline data that also enables fast online fine-tuning capabilities.

Further, we are interested in algorithms that enjoy sample efficiency while leveraging (value) function approximation.

Ideally, we would like methods that train LMs only once ( i.e., one-shot) with a fixed objective, as in