DocumentCode :
106189
Title :
Asynchronous Adaptation and Learning Over Networks—Part II: Performance Analysis
Author :
Xiaochuan Zhao ; Sayed, Ali H.
Author_Institution :
Dept. of Electr. Eng., Univ. of California, Los Angeles, Los Angeles, CA, USA
Volume :
63
Issue :
4
fYear :
2015
fDate :
Feb.15, 2015
Firstpage :
827
Lastpage :
842
Abstract :
In Part I of this paper, also in this issue, we introduced a fairly general model for asynchronous events over adaptive networks including random topologies, random link failures, random data arrival times, and agents turning on and off randomly. We performed a stability analysis and established the notable fact that the network is still able to converge in the mean-square-error sense to the desired solution. Once stable behavior is guaranteed, it becomes important to evaluate how fast the iterates converge and how close they get to the optimal solution. This is a demanding task due to the various asynchronous events and due to the fact that agents influence each other. In this Part II, we carry out a detailed analysis of the mean-square-error performance of asynchronous strategies for solving distributed optimization and adaptation problems over networks. We derive analytical expressions for the mean-square convergence rate and the steady-state mean-square-deviation. The expressions reveal how the various parameters of the asynchronous behavior influence network performance. In the process, we establish the interesting conclusion that even under the influence of asynchronous events, all agents in the adaptive network can still reach an O(ν1 + γo´) near-agreement with some γo´ > 0 while approaching the desired solution within O(ν) accuracy, where ν is proportional to the small step-size parameter for adaptation.
Keywords :
learning (artificial intelligence); mean square error methods; multi-agent systems; network theory (graphs); adaptation problems; adaptive networks; asynchronous adaptation; asynchronous events; distributed optimization problems; learning; mean-square convergence rate; mean-square-error stability; network performance; performance analysis; random data arrival time; random link failure; random topology; stability analysis; steady-state mean-square-deviation; step-size parameter; Asymptotic stability; Convergence; Covariance matrices; Noise; Stability analysis; Steady-state; Vectors; Adaptive networks; asynchronous behavior; diffusion adaptation; distributed learning; distributed optimization; dynamic topology; link failures;
fLanguage :
English
Journal_Title :
Signal Processing, IEEE Transactions on
Publisher :
ieee
ISSN :
1053-587X
Type :
jour
DOI :
10.1109/TSP.2014.2385041
Filename :
6994875
Link To Document :
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