Optimal Single-Choice Prophet Inequalities from Samples

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 ε>0, O(n) samples from the distribution suffice to achieve the optimal competitive ratio (≈0.745) within (1+ε), resolving an open problem of Correa, Dütting, Fischer, and Schewior.