Rate-Optimal Bayesian Simple Regret in Best Arm Identification

• 成果类型: Article
• 署名作者: Komiyama, Junpei; Ariu, Kaito; Kato, Masahiro; Qin, Chao
• 署名单位: New York University; Royal Institute of Technology; Columbia University
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2022.0011
• 发表日期: 2024
• 页码: 1629-1646
• 关键词: multiarmed bandit; convergence-rates; allocation; elimination; algorithms; DESIGN

摘要

We consider best arm identification in the multiarmed bandit problem. Assuming certain continuity conditions of the prior, we characterize the rate of the Bayesian simple regret. Differing from Bayesian regret minimization, the leading term in the Bayesian simple regret derives from the region in which the gap between optimal and suboptimal p ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi arms is smaller than (log T)/T. We propose a simple and easy-to-compute algorithm with its leading term matching with the lower bound up to a constant factor; simulation results support our theoretical findings.