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Bayesian Optimization Under Uncertainty for Chance Constrained Problems

Abstract : Chance constraint is an important tool for modeling the reliability on decision making in the presence of uncertainties. Indeed, the chance constraint enforces that the constraint is satisfied with probability 1 − α ( 0 < α < 1 ) at least. In addition, we consider that the objective func- tion is affected by uncertainties. This problem is challenging since modeling a complex system under uncertainty can be expensive and for most real-world stochastic optimization will not be computationally viable. In this talk, we propose a Bayesian methodology to efficiently solve such class of problems. The central idea is to use Gaussian Process (GP) models [1] together with appropriate acquisi- tion functions to guide the search for an optimal solution. We first show that by specifying a GP prior to the objective function, the loss function becomes tractable [2]. Similarly, using GP models for the constraints, the probability satisfaction can be efficiently approximated. Sub- sequently, we introduce new acquisition functions to iteratively select the points to query the expensive objective and constraint functions. Finally, we present numerical examples to validate our approach compared to benchmark results.
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Conference papers
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https://hal-emse.ccsd.cnrs.fr/emse-02351011
Contributor : Florent Breuil <>
Submitted on : Wednesday, November 6, 2019 - 11:25:22 AM
Last modification on : Wednesday, August 5, 2020 - 3:43:16 AM

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  • HAL Id : emse-02351011, version 1

Citation

Mohamed Reda El Amri, Christophette Blanchet-Scalliet, Celine Helbert, Rodolphe Le Riche. Bayesian Optimization Under Uncertainty for Chance Constrained Problems. PGMO Days 2019, Dec 2019, Palaiseau, France. ⟨emse-02351011⟩

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