Convergence rate of discrete-time stochastic approximation type consensus algorithms

Huaibin Tang; Tao Li

doi:10.1016/j.ifacol.2015.10.328

Convergence rate of discrete-time stochastic approximation type consensus algorithms

Huaibin Tang, Tao Li

Research output: Contribution to journal › Conference article › peer-review

1 Scopus citations

Abstract

In this paper, we study the convergence rate of the distributed stochastic approximation (SA) type algorithm for the discrete-time multi-agent consensus with communication noises. Basic results of algebraic graph theory and probability limit theory are used to study the closed-form solution of the consensus error. Under mild conditions on the decreasing step size and the network topology, we give upper bounds for the mean square and almost sure convergence rates of the consensus errors. Furthermore, for the case with balanced graphs, the exact convergence rate is provided for the mean square of the consensus error.

Original language	English
Pages (from-to)	186-190
Number of pages	5
Journal	IFAC-PapersOnLine
Volume	28
Issue number	22
DOIs	https://doi.org/10.1016/j.ifacol.2015.10.328
State	Published - 1 Oct 2015
Externally published	Yes
Event	5th IFAC Workshop on Distributed Estimation and Control in Networked Systems, NecSys 2015 - Philadelphia, United States Duration: 10 Sep 2015 → 11 Sep 2015

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10.1016/j.ifacol.2015.10.328

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abstract = "In this paper, we study the convergence rate of the distributed stochastic approximation (SA) type algorithm for the discrete-time multi-agent consensus with communication noises. Basic results of algebraic graph theory and probability limit theory are used to study the closed-form solution of the consensus error. Under mild conditions on the decreasing step size and the network topology, we give upper bounds for the mean square and almost sure convergence rates of the consensus errors. Furthermore, for the case with balanced graphs, the exact convergence rate is provided for the mean square of the consensus error.",

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AB - In this paper, we study the convergence rate of the distributed stochastic approximation (SA) type algorithm for the discrete-time multi-agent consensus with communication noises. Basic results of algebraic graph theory and probability limit theory are used to study the closed-form solution of the consensus error. Under mild conditions on the decreasing step size and the network topology, we give upper bounds for the mean square and almost sure convergence rates of the consensus errors. Furthermore, for the case with balanced graphs, the exact convergence rate is provided for the mean square of the consensus error.

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Convergence rate of discrete-time stochastic approximation type consensus algorithms

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