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Conference Papers Year : 2019

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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Dates and versions

emse-02351011 , version 1 (06-11-2019)

Identifiers

  • HAL Id : emse-02351011 , version 1

Cite

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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