Optimal Stopping of a Random Sequence with Unknown Distribution

• 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: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2020.1109
• 发表日期: 2022
• 页码: 29-49
• 关键词: optimal selection; CHOICE

摘要

The subject of this paper is the problem of optimal stopping of a sequence of independent and identically distributed random variables with unknown distribution. We propose a stopping rule that is based on relative ranks and study its performance as measured by the maximal relative regret over suitable nonparametric classes of distributions. It is shown that the proposed rule is first-order asymptotically optimal and nearly rate optimal in terms of the rate at which the relative regret converges to zero. We also develop a general method for numerical solution of sequential stopping problems with no distributional information and use it in order to implement the proposed stopping rule. Some numerical experiments illustrating performance of the rule are presented as well.