  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.
