A note on optimal strategies of a generalized two-stage bandit problem

Abstract

In Yue [Yue, J. C. (1999). Generalized two-stage bandit problem. Commun. Statist. Theo. Meth. 28(9):2261-2276], a two-stage approach was used to explore the Bernoulli two-armed bandit problem, where he assumed that one arm has a smaller prior variance than the other arm. In this paper, adapting Yue`s assumption, we study the structure of the optimal strategy, which maximizes the expected number of successes. We confirm the conjecture of Pearson [Pearson, L. M. (1980). Treatment Allocation for Clinical Trials in Stages. Ph.D. thesis, University of Minnesota] that it is never optimal to allocate an equal number of observations to two identical arms in the first stage.