Optimal convergence rates of totally asynchronous optimization

Asynchronous optimization algorithms are at the core of modern machine learning and resource allocation systems. However, most convergence results consider bounded information delays and several important algorithms lack guarantees when they operate under total asynchrony. In this paper, we derive e...

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Vydané v:Proceedings of the IEEE Conference on Decision & Control s. 6484 - 6490
Hlavní autori: Wu, Xuyang, Magnusson, Sindri, Reza Feyzmahdavian, Hamid, Johansson, Mikael
Médium: Konferenčný príspevok..
Jazyk:English
Vydavateľské údaje: IEEE 06.12.2022
Predmet:
Computational modeling
Delays
Indexes
Machine learning
Machine learning algorithms
Numerical models
Resource management
ISSN:2576-2370
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Abstract Asynchronous optimization algorithms are at the core of modern machine learning and resource allocation systems. However, most convergence results consider bounded information delays and several important algorithms lack guarantees when they operate under total asynchrony. In this paper, we derive explicit convergence rates for the proximal incremental aggregated gradient (PIAG) and the asynchronous block-coordinate descent (Async-BCD) methods under a specific model of total asynchrony, and show that the derived rates are order-optimal. The convergence bounds provide an insightful understanding of how the growth rate of the delays deteriorates the convergence times of the algorithms. Our theoretical findings are demonstrated by a numerical example.
AbstractList Asynchronous optimization algorithms are at the core of modern machine learning and resource allocation systems. However, most convergence results consider bounded information delays and several important algorithms lack guarantees when they operate under total asynchrony. In this paper, we derive explicit convergence rates for the proximal incremental aggregated gradient (PIAG) and the asynchronous block-coordinate descent (Async-BCD) methods under a specific model of total asynchrony, and show that the derived rates are order-optimal. The convergence bounds provide an insightful understanding of how the growth rate of the delays deteriorates the convergence times of the algorithms. Our theoretical findings are demonstrated by a numerical example.
Author Wu, Xuyang
Johansson, Mikael
Magnusson, Sindri
Reza Feyzmahdavian, Hamid
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  givenname: Sindri
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  givenname: Hamid
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  givenname: Mikael
  surname: Johansson
  fullname: Johansson, Mikael
  email: mikaelj@kth.se
  organization: KTH Royal Institute of Technology,Division of Decision and Control Systems, School of EECS,Stockholm,Sweden,SE-100 44
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Snippet Asynchronous optimization algorithms are at the core of modern machine learning and resource allocation systems. However, most convergence results consider...
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SubjectTerms Computational modeling
Delays
Indexes
Machine learning
Machine learning algorithms
Numerical models
Resource management
Title Optimal convergence rates of totally asynchronous optimization
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