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