Impact of communication link noise on distributed ATC stochastic optimization: Analysis and algorithmic enhancements

Abstract

This paper investigates two distributed adapt-then-combine stochastic gradient (DATC-SG) algorithms over networks with noisy communication links. Theoretical analysis establishes that, under suitable conditions on the step-size and combination matrix, both algorithms converge in the mean-square-error sense to a neighborhood of the global minimizer. Unlike gradient tracking algorithms, the DATC-SG methods do not require specific initialization and are not affected by the accumulation of link noise. To further enhance performance, improved variants incorporating a moving average mechanism and a link noise attenuation factor are presented. The mean-square convergence of these enhanced algorithms is also analytically verified. Finally, simulation results support the theoretical findings and demonstrate the effectiveness of the proposed methods under link noise scenario.