Risk optimization using the Chernoff bound and stochastic gradient descent

dc.contributor.authorCarlon, Andre Gustavo
dc.contributor.authorKroetz, Henrique Machado
dc.contributor.authorTorii, André Jacomel
dc.contributor.authorLopez, Rafael Holdorf
dc.contributor.authorMiguel, Leandro Fleck Fadel
dc.contributor.departmentComputer, Electrical and Mathematical Science and Engineering (CEMSE) Division
dc.contributor.institutionCenter for Optimization and Reliability in Engineering (CORE), Department of Civil Engineering, Federal University of Santa Catarina, UFSC, Rua João Pio Duarte, s/n, Florianopolis, Brazil
dc.contributor.institutionCenter for Marine Studies, Federal University of Paraná, UFPR, Av Beira Mar, s/n, Pontal do Paraná, Brazil
dc.contributor.institutionLatin American Institute for Technology, Infrastructure and Territory (ILATIT), Federal University for Latin American Integration (UNILA), Av. Tancredo Neves 6731, Foz do Iguaçu, Brazil
dc.date.accessioned2022-05-16T05:32:23Z
dc.date.available2022-05-16T05:32:23Z
dc.date.issued2022-04-20
dc.description.abstractThis 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.
dc.description.sponsorshipFinanced 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.
dc.eprint.versionPost-print
dc.identifier.citationCarlon, 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
dc.identifier.doi10.1016/j.ress.2022.108512
dc.identifier.eid2-s2.0-85129461410
dc.identifier.issn0951-8320
dc.identifier.journalReliability Engineering and System Safety
dc.identifier.pages108512
dc.identifier.urihttp://hdl.handle.net/10754/677931
dc.identifier.volume223
dc.publisherElsevier BV
dc.relation.urlhttps://linkinghub.elsevier.com/retrieve/pii/S0951832022001703
dc.rightsNOTICE: this is the author’s version of a work that was accepted for publication in Reliability Engineering and System Safety. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Reliability Engineering and System Safety, [223, , (2022-04-20)] DOI: 10.1016/j.ress.2022.108512 . © 2022. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
dc.rights.embargodate2024-04-20
dc.titleRisk optimization using the Chernoff bound and stochastic gradient descent
dc.typeArticle
display.details.left<span><h5>Embargo End Date</h5>2024-04-20<br><br><h5>Type</h5>Article<br><br><h5>Authors</h5><a href="https://repository.kaust.edu.sa/search?spc.sf=dc.date.issued&spc.sd=DESC&f.author=Carlon, Andre Gustavo,equals">Carlon, Andre Gustavo</a><br><a href="https://repository.kaust.edu.sa/search?query=orcid.id:0000-0003-3977-1112&spc.sf=dc.date.issued&spc.sd=DESC">Kroetz, Henrique Machado</a> <a href="https://orcid.org/0000-0003-3977-1112" target="_blank"><img src="https://repository.kaust.edu.sa/server/api/core/bitstreams/82a625b4-ed4b-40c8-865a-d6a5225a26a4/content" width="16" height="16"/></a><br><a href="https://repository.kaust.edu.sa/search?spc.sf=dc.date.issued&spc.sd=DESC&f.author=Torii, André Jacomel,equals">Torii, André Jacomel</a><br><a href="https://repository.kaust.edu.sa/search?query=orcid.id:0000-0001-9037-0176&spc.sf=dc.date.issued&spc.sd=DESC">Lopez, Rafael Holdorf</a> <a href="https://orcid.org/0000-0001-9037-0176" target="_blank"><img src="https://repository.kaust.edu.sa/server/api/core/bitstreams/82a625b4-ed4b-40c8-865a-d6a5225a26a4/content" width="16" height="16"/></a><br><a href="https://repository.kaust.edu.sa/search?spc.sf=dc.date.issued&spc.sd=DESC&f.author=Miguel, Leandro Fleck Fadel,equals">Miguel, Leandro Fleck Fadel</a><br><br><h5>KAUST Department</h5><a href="https://repository.kaust.edu.sa/search?spc.sf=dc.date.issued&spc.sd=DESC&f.department=Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division,equals">Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division</a><br><br><h5>Date</h5>2022-04-20</span>
display.details.right<span><h5>Abstract</h5>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.<br><br><h5>Citation</h5>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<br><br><h5>Acknowledgements</h5>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.<br><br><h5>Publisher</h5><a href="https://repository.kaust.edu.sa/search?spc.sf=dc.date.issued&spc.sd=DESC&f.publisher=Elsevier BV,equals">Elsevier BV</a><br><br><h5>Journal</h5><a href="https://repository.kaust.edu.sa/search?spc.sf=dc.date.issued&spc.sd=DESC&f.journal=Reliability Engineering and System Safety,equals">Reliability Engineering and System Safety</a><br><br><h5>DOI</h5><a href="https://doi.org/10.1016/j.ress.2022.108512">10.1016/j.ress.2022.108512</a><br><br><h5>Additional Links</h5>https://linkinghub.elsevier.com/retrieve/pii/S0951832022001703</span>
kaust.personCarlon, Andre Gustavo
orcid.authorCarlon, Andre Gustavo
orcid.authorKroetz, Henrique Machado::0000-0003-3977-1112
orcid.authorTorii, André Jacomel
orcid.authorLopez, Rafael Holdorf::0000-0001-9037-0176
orcid.authorMiguel, Leandro Fleck Fadel
orcid.id0000-0001-9037-0176
orcid.id0000-0003-3977-1112
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