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2021 | OriginalPaper | Chapter

Stochastic Gradient Descent for Risk Optimization

Authors : André Gustavo Carlon, André Jacomel Torii, Rafael Holdorf Lopez, José Eduardo Souza de Cursi

Published in: Proceedings of the 5th International Symposium on Uncertainty Quantification and Stochastic Modelling

Publisher: Springer International Publishing

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Abstract

This paper presents an approach for the use of stochastic gradient descent methods for the solution of risk optimization problems. The first challenge is to avoid the high-cost evaluation of the failure probability and its gradient at each iteration of the optimization process. We propose here that it is accomplished by employing a stochastic gradient descent algorithm for the minimization of the Chernoff bound of the limit state function associated with the probabilistic constraint. The employed stochastic gradient descent algorithm, the Adam algorithm, is a robust method used in machine learning training. A numerical example is presented to illustrate the advantages and potential drawbacks of the proposed approach.

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previous chapter Robust Design of Stochastic Dynamic Systems Based on Fatigue Damage
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Metadata
Title
Stochastic Gradient Descent for Risk Optimization
Authors
André Gustavo Carlon
André Jacomel Torii
Rafael Holdorf Lopez
José Eduardo Souza de Cursi
Copyright Year
2021
Book
Proceedings of the 5th International Symposium on Uncertainty Quantification and Stochastic Modelling

Print ISBN: 978-3-030-53668-8

Electronic ISBN: 978-3-030-53669-5

Copyright Year: 2021

DOI
https://doi.org/10.1007/978-3-030-53669-5_31