Secretary problem with vanishing objects

Сергей Иванович Доценко; Sergey Dotsenko; Георгий Шевченко; Georgiy Shevchenko

doi:10.17076/mgta_2020_2_16

Сергей Иванович Доценко Киевский национальный университет им. Тараса Шевченко
Sergey Dotsenko Taras Shevchenko National University of Kyiv
Георгий Шевченко Киевский национальный университет им. Тараса Шевченко
Georgiy Shevchenko Taras Shevchenko National University of Kyiv

DOI: https://doi.org/10.17076/mgta_2020_2_16

Keywords: optimal selection problem, secretary problem, vanishing objects, large deviation probability

Abstract

We consider a version of the secretary problem where elements may vanish during the selection and become unchoosable. We construct a selection strategy and identify the probability to select the best element, which turns out to be asymptotically maximal as number of elements increases indefinitely. As an auxiliary result of independent interest we establish large deviation probability estimates for sums of independent variables with distinct geometric distribution.