Optimal Bayesian strategies for the infinite-armed Bernoulli bandit
Journal
Journal of Statistical Planning and Inference
Journal Volume
142
Journal Issue
1
Pages
86-94
Date Issued
2012
Author(s)
Hung Y.-C.
Abstract
We consider the bandit problem with an infinite number of Bernoulli arms, of which the unknown parameters are assumed to be i.i.d. random variables with a common distribution F. Our goal is to construct optimal strategies of choosing "arms" so that the expected long-run failure rate is minimized. We first review a class of strategies and establish their asymptotic properties when F is known. Based on the results, we propose a new strategy and prove that it is asymptotically optimal when F is unknown. Finally, we show that the proposed strategy performs well for a number of simulation scenarios. © 2011 Elsevier B.V.
Subjects
Bandit problem; Bayesian strategy; Bernoulli arms; Prior distribution
Type
journal article