Title: Between the Secretary Problem and the Prophet Inequality

Abstract: In both the classical secretary problem and the prophet inequality, we observe a sequence of numbers in an online fashion, and we make an irrevocable decision to select one of the numbers. However, the order in which the numbers appear, how much information we have about the numbers before we observe them, and the objective we desire to maximize are all different in the two problems.
Several models that are in between the secretary problem and the prophet inequality along these dimensions have been previously explored. In this talk, we explain some of the main ideas that allow us to obtain optimal or nearly optimal results for these models.