Optimal Multiple Stopping Rule for Warm-Starting Sequential Selection

In this paper we present the Warm-starting Dynamic Thresholding algorithm, developed using dynamic programming, for a variant of the standard online selection problem. The problem allows job positions to be either free or already occupied at the beginning of the process. Throughout the selection process, the decision maker interviews one after the other the new candidates and reveals a quality score for each of them. Based on that information, she can (re) assign each job at most once by taking immediate and irrevocable decisions. We relax the hard requirement of the class of dynamic programming algorithms to perfectly know the distribution from which the scores of candidates are drawn, by presenting extensions for the partial and no-information cases, in which the decision maker can learn the underlying score distribution sequentially while interviewing candidates.