Influence of Link Noise on Exact Diffusion Stochastic Optimization Over Distributed Networks

In this article, we examine the effect of link noise on the performance of the exact diffusion stochastic gradient (EDSG) procedure for optimization and learning over adaptive networks. First, it is shown through a mean-square-error analysis that for sufficiently small step-size $\mu$ and large iteration number $n$, there is an increase in the mean-square-deviation (MSD) on the order of $n\mu^{\boldsymbol{-}2}$. To address this deterioration, we propose two revised EDSG algorithms. The first approach deals with additive channel noise interference, while the second approach deals with quantization noise interference. The theoretical analysis shows that both algorithms can estimate the optimal parameter with arbitrary accuracy. Computer simulations illustrate the validity of the theoretical findings and the effectiveness of the proposed approaches.