Transfer Q-learning

TL;DR

This paper introduces transfer Q-learning algorithms for time-inhomogeneous finite-horizon MDPs, enabling knowledge transfer across tasks and stages, with theoretical guarantees and empirical validation in complex RL settings.

Contribution

It develops novel transfer Q-learning algorithms with re-targeting for cross-stage and cross-task transfer, providing the first theoretical analysis of transfer learning in RL.

Findings

Faster convergence rate of Q* estimation in offline RL transfer.

Lower regret bounds in offline-to-online RL transfer.

Empirical validation on synthetic and real datasets supports theoretical results.

Abstract

Time-inhomogeneous finite-horizon Markov decision processes (MDP) are frequently employed to model decision-making in dynamic treatment regimes and other statistical reinforcement learning (RL) scenarios. These fields, especially healthcare and business, often face challenges such as high-dimensional state spaces and time-inhomogeneity of the MDP process, compounded by insufficient sample availability which complicates informed decision-making. To overcome these challenges, we investigate knowledge transfer within time-inhomogeneous finite-horizon MDP by leveraging data from both a target RL task and several related source tasks. We have developed transfer learning (TL) algorithms that are adaptable for both batch and online $Q$-learning, integrating valuable insights from offline source studies. The proposed transfer $Q$-learning algorithm contains a novel {\em re-targeting} step that enables {\em cross-stage transfer} along multiple stages in an RL task, besides the usual {\em cross-task transfer} for supervised learning. We establish the first theoretical justifications of TL in RL tasks by showing a faster rate of convergence of the $Q^*$-function estimation in the offline RL transfer, and a lower regret bound in the offline-to-online RL transfer under stage-wise reward similarity and mild design similarity across tasks. Empirical evidence from both synthetic and real datasets is presented to evaluate the proposed algorithm and support our theoretical results.