Data-Driven Knowledge Transfer in Batch $Q^*$ Learning

TL;DR

This paper introduces a framework for transferring knowledge in batch $Q^*$ learning within MDPs, improving decision-making efficiency by leveraging source data to address data scarcity in new tasks.

Contribution

It proposes a Transferred Fitted $Q$-Iteration algorithm with function approximation and analyzes how task discrepancy affects transfer performance.

Findings

The method improves learning error rates over single-task approaches.

Theoretical analysis links performance to task discrepancy and sample sizes.

Empirical results confirm the effectiveness of the transfer approach.

Abstract

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.