Optimal Single-Choice Prophet Inequalities from Samples

Abstract

We study the single-choice Prophet Inequality problem when the gambler is given access to samples. We show that the optimal competitive ratio of $1/2$ can be achieved with a single sample from each distribution. When the distributions are identical, we show that for any constant $\epsilon >0$, $O(n)$ samples from the distribution suffice to achieve the optimal competitive ratio ($\approx 0.745$) within $(1+\epsilon )$, resolving an open problem of Correa, Dütting, Fischer, and Schewior.

Appears in Innovations in Theoretical Computer Science (ITCS) 2020