Convergence properties of the expected improvement algorithm with fixed mean and covariance functions

This paper deals with the convergence of the expected improvement algorithm, a popular global optimization algorithm based on a Gaussian process model of the function to be optimized. The first result is that under some mild hypotheses on the covariance function k of the Gaussian process, the expect...

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Vydáno v:Journal of statistical planning and inference Ročník 140; číslo 11; s. 3088 - 3095
Hlavní autoři: Vazquez, Emmanuel, Bect, Julien
Médium: Journal Article
Jazyk:angličtina
Vydáno: Kidlington Elsevier B.V 01.11.2010
Elsevier
Témata:
Bayesian optimization
Calculus of variations and optimal control
Computer experiments
Exact sciences and technology
Gaussian process
General topics
Global optimization
Machine Learning
Mathematical analysis
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Numerical methods in mathematical programming, optimization and calculus of variations
Numerical methods in optimization and calculus of variations
Optimization and Control
Probability
Probability and statistics
Probability theory and stochastic processes
RKHS
Sciences and techniques of general use
Sequential design
Statistics
Statistics Theory
Stochastic processes
Computer experiments
Global optimization
RKHS
Gaussian process
Sequential design
Bayesian optimization
Density estimation
Covariance function
Optimization method
Gaussian distribution
Probability distribution
Optimization
Convergence
Sequential method
Variational calculus
Hilbert space
Mathematical programming
Bayes estimation
Prior distribution
Continuous function
Statistical decision
Prior probability
Algorithm
Mean estimation
Statistical method
Numerical analysis
Gaussian processes
sequential design
computer experiments
global optimization
ISSN:0378-3758, 1873-1171
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Popis
Shrnutí:This paper deals with the convergence of the expected improvement algorithm, a popular global optimization algorithm based on a Gaussian process model of the function to be optimized. The first result is that under some mild hypotheses on the covariance function k of the Gaussian process, the expected improvement algorithm produces a dense sequence of evaluation points in the search domain, when the function to be optimized is in the reproducing kernel Hilbert space generated by k. The second result states that the density property also holds for P -almost all continuous functions, where P is the (prior) probability distribution induced by the Gaussian process.
ISSN:0378-3758
1873-1171
DOI:10.1016/j.jspi.2010.04.018