Second-Order Guarantees of Distributed Gradient Algorithms

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>

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
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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)

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)

Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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