Study On Minibatch Stochastic ADMM

In this paper we study the optimization problem of composite objective functions with expected terms and linear equality constraints.In order to solve this problem,we propose a Minibatch Stochastic Alternating Direction Method of Multipliers,and at the same time,we give the convergence rate of the method in a expected sense after satisfying some basic assumptions.We replace objective function by it’s first order approximation.This simple modification makes our method applicable to a more gen-eral class of convex objective functions which might not have a closed-form solution in minimizing the augmented lagrangian function directly.Compared with most of the traditional methods,our method does not need to input all the data at one time.We can train a model with a small amount of data and adjust the parameters with new data continuously.This increases the flexibility of the model.Finally,in the numerical ex-periment,we use the Alternating Direction Method of Multipliers(ADMM)and the Stochastic ADMM to do the comparative experiment.It is found that the Minibatch Stochastic ADMM proposed in this paper is effective,and in most cases it has certain advantages.