A geometrically convergent method for distributed optimization over time-varying graphs

Angelia Nedich; Alex Olshevsky; Wei Shi

doi:10.1109/CDC.2016.7798402

A geometrically convergent method for distributed optimization over time-varying graphs

Angelia Nedich, Alex Olshevsky, Wei Shi

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

16 Scopus citations

Abstract

This paper considers the problem of distributed optimization over time-varying undirected graphs. We discuss a distributed algorithm, which we call DIGing, for solving this problem based on a combination of an inexact gradient method and a gradient tracking technique. This algorithm deploys fixed step size but converges exactly to the global and consensual minimizer. Under strong convexity assumption, we prove that the algorithm converges at an R-linear (geometric) convergence rate as long as the step size is less than a specific bound; we give an explicit estimate of this rate over uniformly connected graph sequences and show it scales polynomially with the number of nodes. Numerical experiments demonstrate the efficacy of the introduced algorithm and validate our theoretical findings.

Original language	English (US)
Title of host publication	2016 IEEE 55th Conference on Decision and Control, CDC 2016
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	1023-1029
Number of pages	7
ISBN (Electronic)	9781509018376
DOIs	https://doi.org/10.1109/CDC.2016.7798402
State	Published - Dec 27 2016
Externally published	Yes
Event	55th IEEE Conference on Decision and Control, CDC 2016 - Las Vegas, United States Duration: Dec 12 2016 → Dec 14 2016

Other

Other	55th IEEE Conference on Decision and Control, CDC 2016
Country/Territory	United States
City	Las Vegas
Period	12/12/16 → 12/14/16

ASJC Scopus subject areas

Artificial Intelligence
Decision Sciences (miscellaneous)
Control and Optimization

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10.1109/CDC.2016.7798402

Cite this

Nedich, A, Olshevsky, A & Shi, W 2016, A geometrically convergent method for distributed optimization over time-varying graphs. in 2016 IEEE 55th Conference on Decision and Control, CDC 2016., 7798402, Institute of Electrical and Electronics Engineers Inc., pp. 1023-1029, 55th IEEE Conference on Decision and Control, CDC 2016, Las Vegas, United States, 12/12/16. https://doi.org/10.1109/CDC.2016.7798402

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title = "A geometrically convergent method for distributed optimization over time-varying graphs",

abstract = "This paper considers the problem of distributed optimization over time-varying undirected graphs. We discuss a distributed algorithm, which we call DIGing, for solving this problem based on a combination of an inexact gradient method and a gradient tracking technique. This algorithm deploys fixed step size but converges exactly to the global and consensual minimizer. Under strong convexity assumption, we prove that the algorithm converges at an R-linear (geometric) convergence rate as long as the step size is less than a specific bound; we give an explicit estimate of this rate over uniformly connected graph sequences and show it scales polynomially with the number of nodes. Numerical experiments demonstrate the efficacy of the introduced algorithm and validate our theoretical findings.",

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doi = "10.1109/CDC.2016.7798402",

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booktitle = "2016 IEEE 55th Conference on Decision and Control, CDC 2016",

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N2 - This paper considers the problem of distributed optimization over time-varying undirected graphs. We discuss a distributed algorithm, which we call DIGing, for solving this problem based on a combination of an inexact gradient method and a gradient tracking technique. This algorithm deploys fixed step size but converges exactly to the global and consensual minimizer. Under strong convexity assumption, we prove that the algorithm converges at an R-linear (geometric) convergence rate as long as the step size is less than a specific bound; we give an explicit estimate of this rate over uniformly connected graph sequences and show it scales polynomially with the number of nodes. Numerical experiments demonstrate the efficacy of the introduced algorithm and validate our theoretical findings.

AB - This paper considers the problem of distributed optimization over time-varying undirected graphs. We discuss a distributed algorithm, which we call DIGing, for solving this problem based on a combination of an inexact gradient method and a gradient tracking technique. This algorithm deploys fixed step size but converges exactly to the global and consensual minimizer. Under strong convexity assumption, we prove that the algorithm converges at an R-linear (geometric) convergence rate as long as the step size is less than a specific bound; we give an explicit estimate of this rate over uniformly connected graph sequences and show it scales polynomially with the number of nodes. Numerical experiments demonstrate the efficacy of the introduced algorithm and validate our theoretical findings.

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BT - 2016 IEEE 55th Conference on Decision and Control, CDC 2016

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A geometrically convergent method for distributed optimization over time-varying graphs

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