A Distributed Stochastic Gradient Tracking Method

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

In this paper, we study the problem of distributed multi-agent optimization over a network, where each agent possesses a local cost function that is smooth and strongly convex. The global objective is to find a common solution that minimizes the average of all cost functions. Assuming agents only have access to unbiased estimates of the gradients of their local cost functions, we consider a distributed stochastic gradient tracking method. We show that, in expectation, the iterates generated by each agent are attracted to a neighborhood of the optimal solution, where they accumulate exponentially fast (under a constant step size choice). More importantly, the limiting (expected) error bounds on the distance of the iterates from the optimal solution decrease with the network size, which is a comparable performance to a centralized stochastic gradient algorithm. Numerical examples further demonstrate the effectiveness of the method.

Original languageEnglish (US)
Title of host publication2018 IEEE Conference on Decision and Control, CDC 2018
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages963-968
Number of pages6
ISBN (Electronic)9781538613955
DOIs
StatePublished - Jan 18 2019
Event57th IEEE Conference on Decision and Control, CDC 2018 - Miami, United States
Duration: Dec 17 2018Dec 19 2018

Publication series

NameProceedings of the IEEE Conference on Decision and Control
Volume2018-December
ISSN (Print)0743-1546

Conference

Conference57th IEEE Conference on Decision and Control, CDC 2018
CountryUnited States
CityMiami
Period12/17/1812/19/18

Fingerprint

Stochastic Gradient
Cost functions
Cost Function
Iterate
Optimal Solution
Gradient Algorithm
Stochastic Algorithms
Accumulate
Error Bounds
Limiting
Gradient
Minimise
Numerical Examples
Decrease
Optimization
Estimate
Demonstrate

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization

Cite this

Pu, S., & Nedich, A. (2019). A Distributed Stochastic Gradient Tracking Method. In 2018 IEEE Conference on Decision and Control, CDC 2018 (pp. 963-968). [8618708] (Proceedings of the IEEE Conference on Decision and Control; Vol. 2018-December). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2018.8618708

A Distributed Stochastic Gradient Tracking Method. / Pu, Shi; Nedich, Angelia.

2018 IEEE Conference on Decision and Control, CDC 2018. Institute of Electrical and Electronics Engineers Inc., 2019. p. 963-968 8618708 (Proceedings of the IEEE Conference on Decision and Control; Vol. 2018-December).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Pu, S & Nedich, A 2019, A Distributed Stochastic Gradient Tracking Method. in 2018 IEEE Conference on Decision and Control, CDC 2018., 8618708, Proceedings of the IEEE Conference on Decision and Control, vol. 2018-December, Institute of Electrical and Electronics Engineers Inc., pp. 963-968, 57th IEEE Conference on Decision and Control, CDC 2018, Miami, United States, 12/17/18. https://doi.org/10.1109/CDC.2018.8618708
Pu S, Nedich A. A Distributed Stochastic Gradient Tracking Method. In 2018 IEEE Conference on Decision and Control, CDC 2018. Institute of Electrical and Electronics Engineers Inc. 2019. p. 963-968. 8618708. (Proceedings of the IEEE Conference on Decision and Control). https://doi.org/10.1109/CDC.2018.8618708
Pu, Shi ; Nedich, Angelia. / A Distributed Stochastic Gradient Tracking Method. 2018 IEEE Conference on Decision and Control, CDC 2018. Institute of Electrical and Electronics Engineers Inc., 2019. pp. 963-968 (Proceedings of the IEEE Conference on Decision and Control).
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