A Fully Bayesian Approach to the Efficient Global Optimization Algorithm
Open Access
Author:
Davanloo Tajbakhsh, Sam
Graduate Program:
Statistics
Degree:
Master of Science
Document Type:
Master Thesis
Date of Defense:
None
Committee Members:
James Landis Rosenberger, Thesis Advisor/Co-Advisor
Keywords:
Global optimization geostatistics hierarchical model expected improvement
Abstract:
Finding the global optimum(s) of a non-convex function is of great importance in numerous applications in science and engineering where the function takes the form of an expensive computer code and its inputs are the independent variables. For this type of problem, Jones et al. \cite{Jones1998} proposed the idea of expected improvement (EI) and embedded it in an algorithm called efficient global optimization, or EGO. Neither EI nor EGO consider the uncertainty in the parameter estimates. One way to account for these uncertainties is to use Bootstrapping. In this paper, instead, we formulate the expected improvement method from a fully Bayesian perspective which results in a corresponding Bayesian EGO method. The performance of the proposed Bayesian EGO is illustrated and compared with the classic EGO method of Jones et al. and the bootstrapped EGO of Kleijnen et al. \cite{Kleijnen2012}. Furthermore, we apply the Bayesian EGO algorithm for the optimization of a stochastic inventory simulation model. It is shown how a bayesian approach to EGO allows to optimize not only the expected improvement criterion, but also any function of the posterior predictive density, such as quantile, leading to a bayesian expected quantile improvement method.
