Secretary problem with vanishing objects

Sergey I. Dotsenko^a, Georgiy M. Shevchenko<sup>b

a</sup> Taras Shevchenko National University of Kyiv
^b Taras Shevchenko National University of Kyiv

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.

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

UDC: 519.88/.21
BBK: 22.18

Received: 10.05.2020
Revised: 17.06.2020
Accepted: 25.06.2020