Projection Consensus for Solving Linear Equations over Random Networks

Abstract

Communication plays a vital role for distributed computation over networks, but practical communication networks are random due to link failures, packet dropouts or node recreation, probably with both temporal and spatial dependence. To understand how generic random networks influence distributed computation, we consider distributedly solving linear equations over a *-mixing random network, where each node holds a part of problem data. We investigate the distributed projection consensus algorithm, prove the almost sure convergence to a consensual solution as a function of initial states, and show the exponential convergence rate of the mean-squared error when the network linear equation admits exact solutions. We further give an explicit convergence rate of the mean-squared error with an estimation of the lower and upper bounds for independent and identically distributed (i.i.d.) random graphs. Simulation studies are provided.