Asymptotically Optimal Problem-Dependent Bandit Policies for Transfer Learning

摘要

We study the non-contextual multi-armed bandit problem in a transfer learning setting: before any pulls, the learner is given N’_k i.i.d. samples from each source distribution nu’_k, and the true target distributions nu_k lie within a known distance bound d_k( nu_k, nu’_k) le L_k. In this framework, we first derive a problem-dependent asymptotic lower bound on cumulative regret that extends the classical Lai–Robbins result to incorporate the transfer parameters (d_k,L_k,N’_k). We then propose textsc{KL-UCB-Transfer}, a simple index policy that matches this new bound in the Gaussian case. Finally, we validate our approach via simulations, showing that textsc{KL-UCB-Transfer} significantly outperforms the no-prior baseline when source and target distributions are sufficiently close.