A new strategy for Robbins' problem of optimal stopping

TL;DR

This paper introduces a new stopping rule for Robbins' problem that combines rank-dependent and threshold strategies, achieving a lower expected rank than previous bounds in the full information setting.

Contribution

It presents a novel stopping rule using the planar Poisson approach that improves the known upper bounds on expected rank in Robbins' problem.

Findings

Expected rank of 2.32614 achieved

New stopping rule outperforms previous bounds

Combines rank-dependent and threshold strategies effectively

Abstract

In this article we study the expected rank problem under full information. Our approach uses the planar Poisson approach from Gnedin (2007) to derive the expected rank of a stopping rule that is one of the simplest non-trivial examples combining rank dependent rules with threshold rules. This rule attains an expected rank lower than the best upper bounds obtained in the literature so far, in particular we obtain an expected rank of 2.32614.