Elynn Chen

Elynn Chen, Xi Chen, Wenbo Jing

In data-driven decision-making in marketing, healthcare, and education, it is desirable to utilize a large amount of data from existing ventures to navigate high-dimensional feature spaces and address data scarcity in new ventures. We explore knowledge transfer in dynamic decision-making by concentrating on batch stationary environments and formally defining task discrepancies through the lens of Markov decision processes (MDPs). We propose a framework of Transferred Fitted $Q$-Iteration algorithm with general function approximation, enabling the direct estimation of the optimal action-state function $Q^*$ using both target and source data. We establish the relationship between statistical performance and MDP task discrepancy under sieve approximation, shedding light on the impact of source and target sample sizes and task discrepancy on the effectiveness of knowledge transfer. We show that the final learning error of the $Q^*$ function is significantly improved from the single task rate both theoretically and empirically.

Jinhang Chai, Elynn Chen, Jianqing Fan

In dynamic decision-making scenarios across business and healthcare, leveraging sample trajectories from diverse populations can significantly enhance reinforcement learning (RL) performance for specific target populations, especially when sample sizes are limited. While existing transfer learning methods primarily focus on linear regression settings, they lack direct applicability to reinforcement learning algorithms. This paper pioneers the study of transfer learning for dynamic decision scenarios modeled by non-stationary finite-horizon Markov decision processes, utilizing neural networks as powerful function approximators and backward inductive learning. We demonstrate that naive sample pooling strategies, effective in regression settings, fail in Markov decision processes.To address this challenge, we introduce a novel ``re-weighted targeting procedure'' to construct ``transferable RL samples'' and propose ``transfer deep $Q^*$-learning'', enabling neural network approximation with theoretical guarantees. We assume that the reward functions are transferable and deal with both situations in which the transition densities are transferable or nontransferable. Our analytical techniques for transfer learning in neural network approximation and transition density transfers have broader implications, extending to supervised transfer learning with neural networks and domain shift scenarios. Empirical experiments on both synthetic and real datasets corroborate the advantages of our method, showcasing its potential for improving decision-making through strategically constructing transferable RL samples in non-stationary reinforcement learning contexts.

Elynn Chen, Sai Li, Michael I. Jordan

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.