Offline-Online Reinforcement Learning for Linear Mixture MDPs

TL;DR

This paper introduces an adaptive reinforcement learning algorithm for linear mixture MDPs that effectively leverages offline data when beneficial and defaults to online learning otherwise, with proven theoretical guarantees.

Contribution

The paper presents a novel algorithm that adaptively combines offline and online data for linear mixture MDPs, with regret bounds that clarify when offline data improves learning.

Findings

The algorithm outperforms online-only methods when offline data is informative.

It safely ignores offline data when uninformative, matching online-only performance.

Theoretical regret bounds are established, supported by numerical experiments.

Abstract

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.