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    Stochastic gradient descent for risk optimization

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    Type
    Conference Paper
    Authors
    Carlon, André Gustavo
    Torii, André Jacomel
    Lopez, Rafael Holdorf
    de Cursi, José Eduardo Souza
    KAUST Department
    Computer, Electrical and Mathematical Sciences and Engineering Division (CEMSE)
    Date
    2020-08-20
    Online Publication Date
    2020-08-20
    Print Publication Date
    2021
    Permanent link to this record
    http://hdl.handle.net/10754/665219
    
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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.
    Citation
    Carlon, A. G., Torii, A. J., Lopez, R. H., & de Cursi, J. E. S. (2020). Stochastic Gradient Descent for Risk Optimization. Proceedings of the 5th International Symposium on Uncertainty Quantification and Stochastic Modelling, 424–435. doi:10.1007/978-3-030-53669-5_31
    Publisher
    Springer Nature
    Conference/Event name
    5th International Symposium on Uncertainty Quantification and Stochastic Modelling, Uncertainties 2020
    ISBN
    9783030536688
    DOI
    10.1007/978-3-030-53669-5_31
    Additional Links
    http://link.springer.com/10.1007/978-3-030-53669-5_31
    ae974a485f413a2113503eed53cd6c53
    10.1007/978-3-030-53669-5_31
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