Data-Driven Knowledge Transfer in Batch $Q^*$ Learning
This addresses data scarcity in new ventures for domains like marketing and healthcare by enabling knowledge transfer from existing data, though it is incremental as it builds on existing fitted Q-iteration methods.
The paper tackles the problem of knowledge transfer in batch stationary environments for dynamic decision-making by proposing a Transferred Fitted Q-Iteration algorithm, showing that the learning error of the Q* function is significantly improved from single-task rates both theoretically and empirically.
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.