Study On Information-Adaptive Variants Of The ADMM

In recent years,Alternating Direction Method of Multipliers(ADMM)has received lots of attention in large-scale and data-distributed machine learning applications.How-ever,most of the variants of ADMM,including the classic ADMM,implicitly assume the full accessibility of the real data values,but in reality,there are usually only some noisy estimations of the gradient,and in some cases,there are even only the function values available.Recently,some literatures have researched many variants of ADMM to solve this problem,and established the convergence rate.In this paper,we consider the convex separable program with three blocks and one of the convex function of the objective function is accessible only for the noisy estimation of its gradient.Under this context,we propose a variant of ADMM to solve this problem,and prove that the rate of convergence for the algorithm is O(1/(?)),where N is the number of iterations.