UCSC-SOE-15-05: Determining Convergence in Gaussian Process Surrogate Model Optimization

Nicholas Grunloh and Herbert Lee
04/17/2015 10:41 PM
Applied Mathematics & Statistics
Identifying convergence in numerical optimization is an ever-present, difficult, and often subjective task. The statistical framework of Gaussian process surrogate model optimization provides useful measures for tracking optimization progress; however, the identification of convergence via these criteria has often provided only limited success and often requires a more subjective analysis. Here we develop a novel approach using ideas originally introduced in the field of statistical process control to define a robust convergence criterion based upon the improvement function. The Exponentially Weighted Moving Average (EWMA) chart provides an ideal starting point for adaptation to track convergence via the EWMA convergence chart introduced here.