  The alternating direction method of multipliers (ADMM) is a powerful
optimization solver in machine learning. Recently, stochastic ADMM has been
integrated with variance reduction methods for stochastic gradient, leading to
SAG-ADMM and SDCA-ADMM that have fast convergence rates and low iteration
complexities. However, their space requirements can still be high. In this
paper, we propose an integration of ADMM with the method of stochastic variance
reduced gradient (SVRG). Unlike another recent integration attempt called
SCAS-ADMM, the proposed algorithm retains the fast convergence benefits of
SAG-ADMM and SDCA-ADMM, but is more advantageous in that its storage
requirement is very low, even independent of the sample size $n$. We also
extend the proposed method for nonconvex problems, and obtain a convergence
rate of $O(1/T)$. Experimental results demonstrate that it is as fast as
SAG-ADMM and SDCA-ADMM, much faster than SCAS-ADMM, and can be used on much
bigger data sets.
