Asymptotically Optimal Learning for Parametric Prophet Inequalities (opens in new tab)

We study learning in prophet inequalities with i.i.d. rewards drawn from an exponential-type parametric family with an unknown parameter $\theta$, a class that includes exponential, Pareto, and bounded-support power-family distributions. We first characterize the optimal full-information asymptotic competitive ratio for this family. In the unbounded-support case, the limit is $ {\left({\theta}/({\theta-c_+})\right)^{c_+/\theta}}/ {\Gamma(1-c_+...