_:n21f71838e43942f38d198d09f388ebdexb22
<http://schema.org/description>
"We study a generalization of the secretary problem, where decisions do not\nhave to be made immediately upon candidates' arrivals. After arriving, each\ncandidate stays in the system for some (random) amount of time and then leaves,\nwhereupon the algorithm has to decide irrevocably whether to select this\ncandidate or not. The goal is to maximize the probability of selecting the best\ncandidate overall. We assume that the arrival and waiting times are drawn from\nknown distributions.\n  Our first main result is a characterization of the optimal policy for this\nsetting. We show that when deciding whether to select a candidate it suffices\nto know only the time and the number of candidates that have arrived so far.\nFurthermore, the policy is monotone non-decreasing in the number of candidates\nseen so far, and, under certain natural conditions, monotone non-increasing in\nthe time. Our second main result is proving that when the number of candidates\nis large, a single threshold policy is almost optimal."
<https://api.deepai.org/profile/thomas-kesselheim>