Asymptotically Optimal Problem-Dependent Bandit Policies for Transfer Learning
Abstract
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) <= 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 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 KL-UCB-Transfer significantly outperforms the no-prior baseline when source and target distributions are sufficiently close.
Keywords
Cite
@article{arxiv.2509.19098,
title = {Asymptotically Optimal Problem-Dependent Bandit Policies for Transfer Learning},
author = {Adrien Prevost and Timothee Mathieu and Odalric-Ambrym Maillard},
journal= {arXiv preprint arXiv:2509.19098},
year = {2025}
}