Randomized averaging algorithms, when can errors and unreliabilities just be ignored?
Abstract:
We consider randomized discrete-time consensus systems that preserve the average "on average", and provide a new upper bound on the mean square deviation of the final consensus value from the initial average.
We show that a certain asymptotic accuracy can be guaranteed when there are few simultaneous interactions or when the simultaneous interactions are sufficiently uncorrelated. Our results are easily applicable to many classes of systems, and we particularize them to various algorithms having been proposed in the literature, obtaining bounds that match or outperform all previously available ones.
Biography:
Julien M. Hendrickx received an engineering degree in applied mathematics and a PhD in mathematical engineering from the Université catholique de Louvain, Belgium, in 2004 and 2008, respectively.
He has been a visiting researcher at the University of Illinois at Urbana Champaign in 2003-2004, at the National ICT Australia in 2005 and 2006, and at the Massachusetts Institute of Technology in 2006 and 2008. He was a postdoctoral fellow at the Laboratory for Information and Decision Systems of the Massachusetts Institute of Technology 2009 and 2010, holding postdoctoral fellowships of the F.R.S.-FNRS (Fund for Scientific Research) and of Belgian American Education Foundation. Since September 2010, he is assistant professor (chargé de cours) at the Université catholique de Louvain, in the Ecole Polytechnique de Louvain.
Doctor Hendrickx is the recipient of the 2008 EECI award for the best PhD thesis in Europe in the field of Embedded and Networked Control, and of the Alcatel-Lucent-Bell 2009 award for a PhD thesis on original new concepts or application in the domain of information or communication technologies.