Risk optimization using the Chernoff bound and stochastic gradient descent

Carlon, André Gustavo, Henrique Machado Kroetz, Torii, André Jacomel, Rafael Holdorf Lopez and Leandro Fleck Fadel Miguel

Reliability Engineering and System Safety, 2022, vol. 223, issue C

Abstract: This paper proposes a stochastic gradient based method for the solution of Risk Optimization (RO) problems. The proposed approach approximates the probability of failure evaluation by an expectation computation with the aid of the Chernoff bound. The resulting approximate problem is then solved using a Stochastic Gradient Descent (SGD) algorithm. Computational efficiency comes from the fact that the Chernoff bound avoids not only the direct computation of the failure probabilities during the optimization process, but also the computation of their gradients with respect to the design variables. Finally, to ensure the quality of the failure probability approximation, we propose a procedure to iteratively adjust the Chernoff bound parameters during the optimization procedure. Three numerical examples are presented to validate the methodology. The proposed approach succeeded in converging to the optimal solution in all cases.

Keywords: Risk optimization; Chernoff bound; Stochastic gradient descent; Stochastic optimization (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:reensy:v:223:y:2022:i:c:s0951832022001703

DOI: 10.1016/j.ress.2022.108512

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