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Coupling and selecting constraints in Bayesian optimization under uncertainties

Abstract : We consider chance constrained optimization where it is sought to optimize a function while complying with constraints, both of which are affected by uncertainties. The high computational cost of realistic simulations strongly limits the number of evaluations and makes this type of problems particularly challenging. In such a context, it is common to rely on Bayesian optimization algorithms. Assuming, without loss of generality, that the uncertainty comes from some of the inputs, it becomes possible to build a Gaussian process model in the joint space of design and uncertain variables. A two-step acquisition function is then used to provide, both, promising optimization variables associated to relevant uncertain samples. Our overall contribution is to correlate the constraints in the GP model and exploit this to optimally decide, at each iteration, which constraint should be evaluated and at which point. The coupled Gaussian model of the constraints relies on an output-as-input encoding. The constraint selection idea is developed by enabling that each constraint can be evaluated for a different uncertain input, thus improving the refinement efficiency. Constraints coupling and selection are gradually implement in 3 algorithm variants which are compared to a reference Bayesian approach. The results are promising in terms of convergence speed, accuracy and stability as observed on a 2, a 4 and a 27-dimensional problems.
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Preprints, Working Papers, ...
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https://hal-emse.ccsd.cnrs.fr/emse-03657028
Contributor : Florent Breuil Connect in order to contact the contributor
Submitted on : Monday, May 2, 2022 - 3:36:58 PM
Last modification on : Saturday, September 24, 2022 - 3:36:05 PM

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  • HAL Id : emse-03657028, version 1
  • ARXIV : 2204.00527

Citation

Julien Pelamatti, Rodolphe Le Riche, Céline Helbert, Christophette Blanchet-Scalliet. Coupling and selecting constraints in Bayesian optimization under uncertainties. {date}. ⟨emse-03657028⟩

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