Bayesian Adaptive Reconstruction of Profile Optima and Optimizers

David Ginsbourger, Jean Baccou, Clément Chevalier, Frédéric Perales, Nicolas Garland & Yann Monerie

Abstract Given a function depending both on decision parameters and nuisance variables, we consider the issue of estimating and quantifying uncertainty on profile optima and/or optimal points as functions of the nuisance variables. The proposed methods are based on interpolations of the objective function constructed from a finite set of evaluations. Here the functions of interest are reconstructed relying on a kriging model but also using Gaussian random field conditional simulations that allow a quantification of uncertainties in the Bayesian framework. Besides this, we introduce a variant of the expected improvement criterion, which proves efficient for adaptively learning the set of profile optima and optimizers. The results are illustrated with a toy example and through a physics case study on the optimal packing of polydisperse frictionless spheres.
Citation Ginsbourger, D., Baccou, J., Chevalier, C., Perales, F., Garland, N., & Monerie, Y. (2014). Bayesian Adaptive Reconstruction of Profile Optima and Optimizers. SIAM/ASA J. Uncertainty Quantification, 2(1), 490-510.
Type Journal article (English)
Date of appearance 2014
Journal SIAM/ASA J. Uncertainty Quantification
Volume 2
Issue 1
Pages 490-510
URL http://epubs.siam.org/doi/abs/10.1137/130949555