The Secretary Problem with Distributions

TL;DR

This paper investigates a variant of the secretary problem with candidates from independent, non-identical distributions, demonstrating that optimal strategies can match those in the IID case, thus resolving a prior conjecture.

Contribution

It proves that non-identical distributions do not reduce the optimal success probability compared to the IID case, confirming a conjecture in the field.

Findings

Optimal success probability matches IID case

Resolves a conjecture by Esfandiari et al.

Extends secretary problem analysis to independent, non-identical distributions

Abstract

We study a variant of the secretary problem where candidates come from independent, not necessarily identical distributions known to us, and show that we can do at least as well as in the IID setting. This resolves a conjecture of Esfandiari et al.