A faster stochastic alternating direction method for large scale convex composite problems

Inspired by the fact that certain randomization schemes incorporated into the stochastic (proximal) gradient methods allow for a large reduction in computational time, we incorporate such a scheme into stochastic alternating direction method of multipliers (ADMM), yielding a faster stochastic alternating direction method (FSADM) for solving a class of large scale convex composite problems. In the numerical experiments, we observe a reduction of this method in computational time compared to previous methods. More importantly, we unify the stochastic ADMM for solving general convex and strongly convex composite problems (i.e., the iterative scheme does not change when the the problem goes from strongly convex to general convex). In addition, we establish the convergence rates of FSADM for these two cases.

Automated summary

This paper introduces a faster stochastic alternating direction method for solving large scale convex composite problems, incorporating a randomization scheme to reduce computational time. The method is shown to be effective in numerical experiments and has unified the stochastic ADMM for solving general convex and strongly convex composite problems.