Distributed Learning Over Networks: Effect of Using Historical Observations

This article investigates the problem of distributed hypothesis testing over networks. By introducing double and triple cumulations of historical observations, two novel distributed learning algorithms are developed to solve the considered problem. Within this framework, we study the convergence rates of the proposed algorithms. More specifically: 1) It is proven that the algorithm with double cumulation of historical observations has a faster convergence rate than those of the existing algorithms. 2) Furthermore, it is proven that the algorithm with triple cumulation of historical observations can be further accelerated. Especially, based on the theoretical results, this article shows that a tradeoff among convergence rate, transient performance, and memory burden exists in the proposed algorithms. Finally, simulation examples verify the theoretical results.