Ergodic Randomized Algorithms and Dynamics Over Networks

Algorithms and dynamics over networks often involve randomization and randomization can induce oscillating dynamics that fail to converge in a deterministic sense. Under assumptions of independence across time and linearity of the updates, we show that the oscillations are ergodic if the expected dy...

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Bibliographic Details
Published in:IEEE transactions on control of network systems Vol. 2; no. 1; pp. 78 - 87
Main Authors: Ravazzi, Chiara, Frasca, Paolo, Tempo, Roberto, Ishii, Hideaki
Format: Journal Article
Language:English
Published: Piscataway IEEE 01.03.2015
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Clocks
Control systems
Convergence
Heuristic algorithms
Power system dynamics
Random variables
Vectors
Randomized algorithms
opinion dynamics
PageRank problem
networks
ISSN:2325-5870, 2372-2533
Online Access:Get full text
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Summary:Algorithms and dynamics over networks often involve randomization and randomization can induce oscillating dynamics that fail to converge in a deterministic sense. Under assumptions of independence across time and linearity of the updates, we show that the oscillations are ergodic if the expected dynamics is stable. We apply this result to three problems of network systems, namely, the estimation from relative measurements, the PageRank computation, and the dynamics of opinions in social networks. In these applications, the randomized dynamics is the asynchronous counterpart of a deterministic (stable) synchronous one. By ergodicity, the deterministic limit can be recovered via a time-averaging operation, which can be performed locally by each node of the network.
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ISSN:2325-5870
2372-2533
DOI:10.1109/TCNS.2014.2367571