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    Courant Institute, New York University

    Natural evolution strategies converge on sphere functions

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    This theoretical investigation gives the first proof of convergence for (radial) natural evolution strategies, on d-dimensional sphere functions, and establishes the conditions on hyper-parameters, as a function of d. For the limit case of large population sizes, we show an asymptotic linear converge rate of 1/2, and in the limit of small learning rates we give a full analytic characterization of the algorithm dynamics, decomposed into transient and asymptotic phases. Finally, we show why omitting the natural gradient from the algorithm is catastrophic.

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    Description

    Title : Natural evolution strategies converge on sphere functions
    Author(s) : Tom Schaul
    Abstract : This theoretical investigation gives the first proof of convergence for (radial) natural evolution strategies, on d-dimensional sphere functions, and establishes the conditions on hyper-parameters, as a function of d. For the limit case of large population sizes, we show an asymptotic linear converge rate of 1/2, and in the limit of small learning rates we give a full analytic characterization of the algorithm dynamics, decomposed into transient and asymptotic phases. Finally, we show why omitting the natural gradient from the algorithm is catastrophic.
    Subject : unspecified
    Area : Other
    Language : English
    Year : 2012

    Affiliations Courant Institute, New York University
    Conference_title : Proceedings of the fourteenth international conference on Genetic and evolutionary computation conference GECCO 12
    Publisher : ACM Press
    City : New York, New York, USA
    Pages : 329 -
    Url : http://dl.acm.org/citation.cfm?doid=2330163.2330211
    Isbn : 9781450311779
    Doi : 10.1145/2330163.2330211

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