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We consider the problem of chance constrained optimization where it is sought to optimize a function and satisfy constraints, both of which are affected by uncertainties. The real world declinations of this problem are particularly challenging because of their inherent computational cost.
To tackle such problems, we propose a new Bayesian optimization method. It applies to the situation where the uncertainty comes from some of the inputs, so that it becomes possible to define an acquisition criterion in the joint optimized-uncertain input space. The main contribution of this work is an acquisition criterion that accounts for both the average improvement in objective function and the constraint reliability. The criterion is derived following the Stepwise Uncertainty Reduction logic and its maximization provides both optimal design variables and uncertain parameters. Analytical expressions are given to efficiently calculate the criterion. Numerical studies on test functions are presented. It is found through experimental comparisons with alternative sampling criteria that the adequation between the sampling criterion and the problem contributes to the efficiency of the overall optimization.
El Amri, Reda 1 ; Le Riche, Rodolphe 2 ; Helbert, Céline 3 ; Blanchet-Scalliet, Christophette 3 ; Da Veiga, Sébastien 4
@article{SMAI-JCM_2023__9__285_0,
author = {El Amri, Reda and Le Riche, Rodolphe and Helbert, C\'eline and Blanchet-Scalliet, Christophette and Da Veiga, S\'ebastien},
title = {A {Sampling} {Criterion} for {Constrained} {Bayesian} {Optimization} with {Uncertainties}},
journal = {The SMAI Journal of computational mathematics},
pages = {285--309},
publisher = {Soci\'et\'e de Math\'ematiques Appliqu\'ees et Industrielles},
volume = {9},
year = {2023},
doi = {10.5802/smai-jcm.102},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.5802/smai-jcm.102/}
}
TY - JOUR AU - El Amri, Reda AU - Le Riche, Rodolphe AU - Helbert, Céline AU - Blanchet-Scalliet, Christophette AU - Da Veiga, Sébastien TI - A Sampling Criterion for Constrained Bayesian Optimization with Uncertainties JO - The SMAI Journal of computational mathematics PY - 2023 SP - 285 EP - 309 VL - 9 PB - Société de Mathématiques Appliquées et Industrielles UR - http://geodesic.mathdoc.fr/articles/10.5802/smai-jcm.102/ DO - 10.5802/smai-jcm.102 LA - en ID - SMAI-JCM_2023__9__285_0 ER -
%0 Journal Article %A El Amri, Reda %A Le Riche, Rodolphe %A Helbert, Céline %A Blanchet-Scalliet, Christophette %A Da Veiga, Sébastien %T A Sampling Criterion for Constrained Bayesian Optimization with Uncertainties %J The SMAI Journal of computational mathematics %D 2023 %P 285-309 %V 9 %I Société de Mathématiques Appliquées et Industrielles %U http://geodesic.mathdoc.fr/articles/10.5802/smai-jcm.102/ %R 10.5802/smai-jcm.102 %G en %F SMAI-JCM_2023__9__285_0
El Amri, Reda; Le Riche, Rodolphe; Helbert, Céline; Blanchet-Scalliet, Christophette; Da Veiga, Sébastien. A Sampling Criterion for Constrained Bayesian Optimization with Uncertainties. The SMAI Journal of computational mathematics, Tome 9 (2023), pp. 285-309. doi: 10.5802/smai-jcm.102
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