Optimal random perturbations for stochastic approximation using a simultaneous perturbation gradient approximation

Payman Sadegh, J. C. Spall

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    Abstract

    The simultaneous perturbation stochastic approximation (SPSA) algorithm has recently attracted considerable attention for optimization problems where it is difficult or impossible to obtain a direct gradient of the objective (say, loss) function. The approach is based on a highly efficient simultaneous perturbation approximation to the gradient based on loss function measurements. SPSA is based on picking a simultaneous perturbation (random) vector in a Monte Carlo fashion as part of generating the approximation to the gradient. This paper derives the optimal distribution for the Monte Carlo process. The objective is to minimize the mean square error of the estimate. We also consider maximization of the likelihood that the estimate be confined within a bounded symmetric region of the true parameter. The optimal distribution for the components of the simultaneous perturbation vector is found to be a symmetric Bernoulli in both cases. We end the paper with a numerical study related to the area of experiment design
    Original languageEnglish
    Title of host publicationAmerican Control Conference, 1997. Proceedings of the 1997
    Volume6
    PublisherIEEE
    Publication date1997
    Pages3582-3586
    ISBN (Print)0-7803-3832-4
    DOIs
    Publication statusPublished - 1997
    Event1997 American Control Conference - Albuquerque, NM, United States
    Duration: 4 Jun 19976 Jun 1997
    http://www.ece.unm.edu/controls/ACC97/welcome.html

    Conference

    Conference1997 American Control Conference
    CountryUnited States
    CityAlbuquerque, NM
    Period04/06/199706/06/1997
    Internet address

    Bibliographical note

    Copyright: 1997 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE

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