The Local Time Method for Targeting and Selection

Abstract

We propose a framework for "targeting and selection" (T&S), a new problem class in simulation optimization where the objective is to select a simulation alternative whose mean performance matches a pre-specified target as closely as possible. T&S resembles the more wellknown problem of ranking and selection, but presents unexpected challenges: for example, a one-step look-ahead method may produce statistically inconsistent estimates of the values, even under very standard normality assumptions. We create a new and fundamentally different approach, based on a Brownian local time model, that exhibits characteristics of two widely-studied methodologies, namely expected improvement and optimal computing budget allocation. We characterize the asymptotic sampling rates of this method and relate them to the convergence rates of metrics of interest. The local time method outperforms benchmarks in experiments, including problems where the modeling assumptions of T&S are violated.