Best Arm Identification under Additive Transfer Bandits

Abstract: We consider a variant of the best arm identification (BAI) problem in multi-armed bandits (MAB) in which there are two sets of arms (source and target), and the objective is to determine the best target arm while only pulling source arms. In this paper, we study the setting when, despite the means being unknown, there is a known additive relationship between the source and target MAB instances. We show how our framework covers a range of previously studied pure exploration problems and additionally captures new problems. We propose and theoretically analyze an LUCB-style algorithm to identify an $\epsilon$-optimal target arm with high probability. Our theoretical analysis highlights aspects of this transfer learning problem that do not arise in the typical BAI setup, and yet recover the LUCB algorithm for single domain BAI as a special case.