Pandora's Problem with Nonobligatory Inspection: Optimal Structure and a PTAS

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 by Doval (2018), and by recent work of Fu Li and Liu (2022), finding the optimal solution is NP-hard.