MINIMIZING THE TIME TO A DECISION

• 成果类型: Article
• 署名作者: Jacka, Saul; Warren, Jon; Windridge, Peter
• 署名单位: University of Warwick
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/10-AAP737
• 发表日期: 2011
• 页码: 1795-1826
• 关键词: perturbed brownian-motion; diffusion-processes; multiarmed bandits; EQUATIONS

摘要

Suppose we have three independent copies of a regular diffusion on [0, 1] with absorbing boundaries. Of these diffusions, either at least two are absorbed at the upper boundary or at least two at the lower boundary. In this way, they determine a majority decision between 0 and 1. We show that the strategy that always runs the diffusion whose value is currently between the other two reveals the majority decision whilst minimizing the total time spent running the processes.