A Fixed-Point Analysis of Regularized Dual Averaging under Static Scenarios

Masahiro Yukawa, Isao Yamada

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Abstract

    In this paper, we analyze the properties of a fixed point of a certain mapping that is implicitly used in each of the regularized dual averaging (RDA) and projection-based RDA (PDA) algorithms. It turns out that, if the loss function has a nonexpansive (1-Lipschltz) gradient such as in the case of a half squared-distance function, RDA converges to a minimizer of the penalized loss function under a restrictive condition. Meanwhile, the fixed point for PDA gives a minimizer of the 'unpenalized' loss function. Some simulation studies are also presented to support the theoretical findings.

    Original languageEnglish
    Title of host publication2018 Asia-Pacific Signal and Information Processing Association Annual Summit and Conference, APSIPA ASC 2018 - Proceedings
    PublisherInstitute of Electrical and Electronics Engineers Inc.
    Pages207-211
    Number of pages5
    ISBN (Electronic)9789881476852
    DOIs
    Publication statusPublished - 2019 Mar 4
    Event10th Asia-Pacific Signal and Information Processing Association Annual Summit and Conference, APSIPA ASC 2018 - Honolulu, United States
    Duration: 2018 Nov 122018 Nov 15

    Publication series

    Name2018 Asia-Pacific Signal and Information Processing Association Annual Summit and Conference, APSIPA ASC 2018 - Proceedings

    Conference

    Conference10th Asia-Pacific Signal and Information Processing Association Annual Summit and Conference, APSIPA ASC 2018
    CountryUnited States
    CityHonolulu
    Period18/11/1218/11/15

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    ASJC Scopus subject areas

    • Information Systems

    Cite this

    Yukawa, M., & Yamada, I. (2019). A Fixed-Point Analysis of Regularized Dual Averaging under Static Scenarios. In 2018 Asia-Pacific Signal and Information Processing Association Annual Summit and Conference, APSIPA ASC 2018 - Proceedings (pp. 207-211). [8659576] (2018 Asia-Pacific Signal and Information Processing Association Annual Summit and Conference, APSIPA ASC 2018 - Proceedings). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.23919/APSIPA.2018.8659576