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Analysis of Distributed ADMM Algorithm for Consensus Optimization in Presence of Node Error

Majzoobi, Layla and Lahouti, Farshad and Shah-Mansouri, Vahid (2019) Analysis of Distributed ADMM Algorithm for Consensus Optimization in Presence of Node Error. IEEE Transactions on Signal Processing, 67 (7). pp. 1774-1784. ISSN 1053-587X. http://resolver.caltech.edu/CaltechAUTHORS:20190131-131444779

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Abstract

Alternating direction method of multipliers (ADMM) is a popular convex optimization algorithm, which can be employed for solving distributed consensus optimization problems. In this setting, agents locally estimate the optimal solution of an optimization problem and exchange messages with their neighbors over a connected network. The distributed algorithms are typically exposed to different types of errors in practice, e.g., due to quantization or communication noise or loss. We here focus on analyzing the convergence of distributed ADMM for consensus optimization in the presence of additive random node error, in which case the nodes communicate a noisy version of their latest estimate of the solution to their neighbors in each iteration. We present analytical upper and lower bounds on the mean-squared steady-state error of the algorithm in case the local objective functions are strongly convex and have Lipschitz continuous gradients. In addition, we show that when the local objective functions are convex and the additive node error is bounded, the estimation error of the noisy ADMM for consensus optimization is also bounded. Numerical results are provided, which demonstrates the effectiveness of the presented analyses and shed light on the role of the system and network parameters on performance.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1109/tsp.2019.2896266DOIArticle
https://arxiv.org/abs/1901.02436arXivDiscussion Paper
ORCID:
AuthorORCID
Majzoobi, Layla0000-0002-2890-6694
Lahouti, Farshad0000-0002-8729-873X
Shah-Mansouri, Vahid0000-0003-4810-491X
Additional Information:© 2019 IEEE. Manuscript received September 10, 2018; revised December 29, 2018; accepted January 10, 2019. Date of publication January 30, 2019; date of current version February 19, 2019. The associate editor coordinating the review of this manuscript and approving it for publication was Dr. Gonzalo Mateos. This paper was presented in part at the IEEE International Conference on Acoustics, Speech, and Signal Processing, Shanghai, China, March 2016.
Subject Keywords:ADMM algorithm, Consensus optimization, Convergence, Node error, Steady State Error
Record Number:CaltechAUTHORS:20190131-131444779
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20190131-131444779
Official Citation:L. Majzoobi, F. Lahouti and V. Shah-Mansouri, "Analysis of Distributed ADMM Algorithm for Consensus Optimization in Presence of Node Error," in IEEE Transactions on Signal Processing, vol. 67, no. 7, pp. 1774-1784, 1 April1, 2019. doi: 10.1109/TSP.2019.2896266
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:92545
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:31 Jan 2019 23:33
Last Modified:26 Feb 2019 19:41

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