An expected improvement criterion for the global optimization of a noisy computer simulator
LE3 .A278 2015
Master of Science
Mathematics and Statistics
Mathematics & Statistics
A computer experiment is often used when physical experimentation is complex, time consuming or expensive. In computer experiments, large computer codes called computer simulators are written to represent numerical models of real phe- nomena. Realistic simulators are often time consuming to run, and thus, we approximate them with surrogate statistical models. In this thesis we consider two surrogates, Gaussian process (GP) models and Bayesian Additive Regression Trees (BART) models. Many simulators are deterministic, that is, re-running the code with the same inputs gives identical results. Yet, it is well known that many simulators often display numerical noise. Rather than lying on a smooth curve, results appear to contain a random scatter about a smooth trend. In this thesis, we focus on minimizing simulator output observed with noise. E cient optimization of an expensive simulator is a challenging problem. Jones, Schonlau & Welch (1998) proposed a merit based criterion called Expected Improvement (EI) for carefully choosing points in a sequential mannner to identify the global minimum of a deterministic simulator. Our objective is to compare the improve- ment functions proposed by Picheny, Ginsbourger, Richet & Caplin (2013) and Ranjan (2013) for global optimization of a noisy simulator. Four test functions are used as simulators for performance comparison, and the EI optimization is done either using a one-shot space- lling design or a genetic algorithm (GA).
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