Bayesian adaptive reconstruction of profile optima and optimizers

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 base 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 field conditional simulations, that allow a quantification of uncertainties in the Bayesian framework. Besides, we elaborate a variant of the Expected Improvement criterion, that proves efficient for adaptively learning the set of profile optima and optimizers. The results are illustrated on a toy example and through a physics case study on the optimal packing of polydisperse frictionless spheres.
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Submitted on : Tuesday, December 17, 2013 - 7:05:03 PM
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David Ginsbourger, Jean Baccou, Clément Chevalier, Frédéric Perales, Nicolas Garland, et al.. Bayesian adaptive reconstruction of profile optima and optimizers. 2013. ⟨hal-00920154⟩

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