Quantile-based optimization of Noisy Computer Experiments with Tunable Precision

Victor Picheny (1) , David Ginsbourger (2) , Yann Richet (3) , Grégory Caplin (3)

1 CERFACS - Centre Européen de Recherche et de Formation Avancée en Calcul Scientifique
2 IMSV - Institute of Mathematical Statistics and Actuarial Science [Bern]
3 IRSN - Institut de Radioprotection et de Sûreté Nucléaire

This article addresses the issue of kriging-based optimization of stochastic simulators. Many of these simulators depend on factors that tune the level of precision of the response, the gain in accuracy being at a price of computational time. The contribution of this work is two-fold: firstly, we propose a quantile-based criterion for the sequential design of experiments, in the fashion of the classical Expected Improvement criterion, which allows an elegant treatment of heterogeneous response precisions. Secondly, we present a procedure for the allocation of the computational time given to each measurement, allowing a better distribution of the computational effort and increased efficiency. Finally, the optimization method is applied to an original application in nuclear criticality safety.

Mots clés: Kriging; Expected Improvement; Stochastic simulators

Domaines: Optimisation et contrôle [math.OC]

Victor Picheny, David Ginsbourger, Yann Richet, Grégory Caplin. Quantile-based optimization of Noisy Computer Experiments with Tunable Precision. 2012. ⟨hal-00578550v3⟩