Performance of a Distributed Stochastic Approximation Algorithm

In this paper, a distributed stochastic approximation algorithm is studied. Applications of such algorithms include decentralized estimation, optimization, control or computing. The algorithm consists in two steps: a local step, where each node in a network updates a local estimate using a stochasti...

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Bibliographic Details
Published in:IEEE transactions on information theory Vol. 59; no. 11; pp. 7405 - 7418
Main Authors: Bianchi, Pascal, Fort, Gersende, Hachem, Walid
Format: Journal Article
Language:English
Published: New York, NY IEEE 01.11.2013
Institute of Electrical and Electronics Engineers
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Applied sciences
Approximation
Approximation algorithms
Approximation methods
Computer Science
Context
Convergence
decentralized estimation
decentralized optimization
Estimation
Exact sciences and technology
gossip algorithms
Information theory
Information, signal and communications theory
Networking and Internet Architecture
Optimization
Optimization algorithms
Ordinary differential equations
Other Statistics
Statistics
stochastic approximation
Stochastic models
Stochastic processes
Telecommunications and information theory
Performance evaluation
Second order
decentralized optimization
Subspace method
Stochastic approximation
Updating
gossip algorithms
Contraction
Optimization
Convergence
Central limit theorem
Decentralized system
Decentralized control
decentralized estimation
Distributed algorithm
Lyapunov function
ISSN:0018-9448, 1557-9654
Online Access:Get full text
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Description
Summary:In this paper, a distributed stochastic approximation algorithm is studied. Applications of such algorithms include decentralized estimation, optimization, control or computing. The algorithm consists in two steps: a local step, where each node in a network updates a local estimate using a stochastic approximation algorithm with decreasing step size, and a gossip step, where a node computes a local weighted average between its estimates and those of its neighbors. Convergence of the estimates toward a consensus is established under weak assumptions. The approach relies on two main ingredients: the existence of a Lyapunov function for the mean field in the agreement subspace, and a contraction property of the random matrices of weights in the subspace orthogonal to the agreement subspace. A second-order analysis of the algorithm is also performed under the form of a central limit Theorem. The Polyak-averaged version of the algorithm is also considered.
Bibliography:SourceType-Scholarly Journals-1
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ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2013.2275131