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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Bibliographic Details
Published in:Proceedings of the IEEE Conference on Decision & Control pp. 6484 - 6490
Main Authors: Wu, Xuyang, Magnusson, Sindri, Reza Feyzmahdavian, Hamid, Johansson, Mikael
Format: Conference Proceeding
Language:English
Published: IEEE 06.12.2022
Subjects:
Computational modeling
Delays
Indexes
Machine learning
Machine learning algorithms
Numerical models
Resource management
ISSN:2576-2370
Online Access:Get full text
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Summary: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.
ISSN:2576-2370
DOI:10.1109/CDC51059.2022.9993168