Risk optimization using the Chernoff bound and stochastic gradient descent

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

Research output: Contribution to journalArticlepeer-review

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.
Original languageEnglish (US)
Pages (from-to)108512
JournalReliability Engineering and System Safety
Volume223
DOIs
StatePublished - Apr 20 2022

ASJC Scopus subject areas

  • Applied Mathematics
  • Industrial and Manufacturing Engineering
  • Safety, Risk, Reliability and Quality

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