WOODROOFE'S ONE-ARMED BANDIT PROBLEM REVISITED

• 成果类型: Article
• 署名作者: Goldenshluger, Alexander; Zeevi, Assaf
• 署名单位: University of Haifa; Columbia University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/08-AAP589
• 发表日期: 2009
• 页码: 1603-1633
• 关键词: INEQUALITIES; allocation

摘要

We consider the one-armed bandit problem of Woodroofe [J. Amer Statist. Assoc. 74 (1979) 799-806], which involves sequential sampling from two populations: one whose characteristics are known, and one which depends on an unknown parameter and incorporates a covariate. The goal is to maximize cumulative expected reward. We study this problem in a minimax setting, and develop rate-optimal polices that involve suitable modifications of the myopic rule. It is shown that the regret, as well as the rate of sampling from the inferior population, can be finite or grow at various rates with the time horizon of the problem, depending on local properties of the covariate distribution. Proofs rely on martingale methods and information theoretic arguments.