Risk optimization using the Chernoff bound and stochastic gradient descent

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

Risk optimization using the Chernoff bound and stochastic gradient descent

Embargo End Date

2024-04-20

Type

Article

Authors

Carlon, Andre Gustavo
Kroetz, Henrique Machado

Torii, André Jacomel
Lopez, Rafael Holdorf

Miguel, Leandro Fleck Fadel

KAUST Department

Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

Date

2022-04-20

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.

Citation

Carlon, A. G., Kroetz, H. M., Torii, A. J., Lopez, R. H., & Miguel, L. F. F. (2022). Risk optimization using the Chernoff bound and stochastic gradient descent. Reliability Engineering & System Safety, 223, 108512. https://doi.org/10.1016/j.ress.2022.108512

Acknowledgements

Financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Brasil (CAPES) - Finance Code 001, and Conselho Nacional de Desenvolvimento Científico e Tecnológico - CNPQ - grant number 307133/2020-6.