Abstract

Gaussian Process models have been used in a number of problems where an objective function f needs to be studied based on a drastically limited number of evaluations. Global optimization algorithms based on Gaussian Process models have been investigated for several decades, and have become quite popular notably in design of computer experiments. Also, further classes of problems involving the estimation of sets implicitly defined by f, e.g. sets of excursion above a given threshold, have inspired multiple research developments. In this talk, we will give an overview of recent results and challenges pertaining to the estimation of sets under Gaussian Process priors, with a particular interest for to the quantification and the sequential reduction of associated uncertainties. Based on a series of joint works primarily with Dario Azzimonti, François Bachoc, Julien Bect, Mickaël Binois, Clément Chevalier, Ilya Molchanov, Victor Picheny, Yann Richet and Emmanuel Vazquez.