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Second-Order Guarantees of Distributed Gradient Algorithms

The result's identifiers

  • Result code in IS VaVaI

    <a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F20%3A00343876" target="_blank" >RIV/68407700:21230/20:00343876 - isvavai.cz</a>

  • Result on the web

    <a href="https://doi.org/10.1137/18M121784X" target="_blank" >https://doi.org/10.1137/18M121784X</a>

  • DOI - Digital Object Identifier

    <a href="http://dx.doi.org/10.1137/18M121784X" target="_blank" >10.1137/18M121784X</a>

Alternative languages

  • Result language

    angličtina

  • Original language name

    Second-Order Guarantees of Distributed Gradient Algorithms

  • Original language description

    We consider distributed smooth nonconvex unconstrained optimization over net- works, modeled as a connected graph. We examine the behavior of distributed gradient-based algorithms near strict saddle points. Specifically, we establish that (i) the renowned distributed gradient descent algorithm likely converges to a neighborhood of a second-order stationary (SoS) solution; and (ii) the more recent class of distributed algorithms based on gradient tracking---implementable also over digraphs---likely converges to exact SoS solutions, thus avoiding (strict) saddle points. Furthermore, new convergence rate results for first-order critical points is established for the latter class of algorithms.

  • Czech name

  • Czech description

Classification

  • Type

    J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database

  • CEP classification

  • OECD FORD branch

    10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Result continuities

  • Project

    <a href="/en/project/EF16_019%2F0000765" target="_blank" >EF16_019/0000765: Research Center for Informatics</a><br>

  • Continuities

    P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Others

  • Publication year

    2020

  • Confidentiality

    S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Data specific for result type

  • Name of the periodical

    SIAM Journal on Optimization

  • ISSN

    1052-6234

  • e-ISSN

    1095-7189

  • Volume of the periodical

    30

  • Issue of the periodical within the volume

    4

  • Country of publishing house

    US - UNITED STATES

  • Number of pages

    40

  • Pages from-to

    3029-3068

  • UT code for WoS article

    000600651900013

  • EID of the result in the Scopus database

    2-s2.0-85096033053