Mathilde Fekom

Mathilde Fekom, Nicolas Vayatis, Argyris Kalogeratos

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.

Mathilde Fekom, Nicolas Vayatis, Argyris Kalogeratos

Under the Dynamic Resource Allocation (DRA) model, an administrator has the mission to allocate dynamically a limited budget of resources to the nodes of a network in order to reduce a diffusion process (DP) (e.g. an epidemic). The standard DRA assumes that the administrator has constantly full information and instantaneous access to the entire network. Towards bringing such strategies closer to real-life constraints, we first present the Restricted DRA model extension where, at each intervention round, the access is restricted to only a fraction of the network nodes, called sample. Then, inspired by sequential selection problems such as the well-known Secretary Problem, we propose the Sequential DRA (SDRA) model. Our model introduces a sequential aspect in the decision process over the sample of each round, offering a completely new perspective to the dynamic DP control. Finally, we incorporate several sequential selection algorithms to SDRA control strategies and compare their performance in SIS epidemic simulations.