Distributed Averaging and Optimization over Random Networks


We study distributed optimization over time-varying and random networks. First, we discuss some new establishments in the study of averaging dynamics over random graphs. In particular, we discuss a necessary condition for ergodicity of distributed averaging dynamics and discuss additional conditions that render this condition sufficient. Then, we consider one of the main applications of the distributed averaging dynamics, i.e., synthesis and analysis of distributed optimization algorithms.  By introducing a new Martingale result, we prove the convergence of a random dynamics to a global minimizer of the distributed optimization problem. We discuss some of the consequences of this result in synthesizing fully distributed algorithms for distributed optimization.


Behrouz Touri received the B.Sc. degree in electrical engineering from the Isfahan University of Technology, Isfahan, Iran, in 2006, the M.Sc. degree in communications, systems, and electronics from Jacobs University, Bremen, Germany, in 2008, and the Ph.D. degree in industrial engineering from the University of Illinois at Urbana–Champaign in 2011. He is an Assistant Professor of the Electrical and Computer Engineering Department with the University of California at San Diego. Prior to that, he was an Assistant Professor of Electrical Engineering with the University of Colorado Boulder. His research interests include applied probability theory, distributed optimization, control and estimation, population dynamics, and evolutionary game theory. He was a recipient of the American Control Council’s Donald P. Eckman Award in 2018 and the AFOSR Young Investigator Award 2016.