Optimal Stopping of a Random Sequence with Unknown Distribution

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)29-49
Number of pages21
JournalMathematics of Operations Research
Issue number1
StatePublished - Feb 2022

Bibliographical note

Funding Information:
Funding: The research was supported [Grants BSF 2010466, ISF 361/15, and NSF CNS-0964170].

Publisher Copyright:
© 2021 INFORMS.


  • Extreme-value distributions
  • Minimax regret
  • No information
  • Optimal stopping
  • Relative ranks
  • Secretary problems

ASJC Scopus subject areas

  • Mathematics (all)
  • Computer Science Applications
  • Management Science and Operations Research


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