Linda Cai, Princeton University

Abstract

Weitzman (1979) introduced Pandora's box problem as a mathematical model of sequential search with inspection costs, in which a searcher is allowed to select a prize from one of n alternatives. Several decades later, Doval (2018) introduced a close version of the problem, where the searcher does not need to incur the inspection cost of an alternative, and can select it uninspected. Unlike the original problem, the optimal solution to the nonobligatory inspection variant is proved to need adaptivity, and by recent work of Fu Li and Liu (2022), finding the optimal solution is NP-hard.

Our first main result is a structural characterization of the optimal policy: We show there exists an optimal policy that follows only two different predetermined orders of inspection, and transitions from one to the other at most once. Our second main result is a polynomial time approximation scheme (PTAS). Our proof involves a novel reduction to a framework developed by Fu Li and Xu (2018), utilizing our optimal two-phase structure. Furthermore, we show Pandora's problem with nonobligatory inspection belongs to class NP, which by using the hardness result of Fu Li and Liu (2022), settles the computational complexity class of the problem.

Joint work with Hedyeh Beyhaghi and to be appeared in STOC 2023.

See: https://theory.cs.rutgers.edu/theory_seminar