Title: Fast Stochastic Variance Reduced ADMM for Stochastic Composition Optimization,
Abstract: We consider the stochastic composition optimization problem proposed in
\cite{wang2017stochastic}, which has applications ranging from estimation to
statistical and machine learning. We propose the first ADMM-based algorithm
named com-SVR-ADMM, and show that com-SVR-ADMM converges linearly for strongly
convex and Lipschitz smooth objectives, and has a convergence rate of $O( \log
S/S)$, which improves upon the $O(S^{-4/9})$ rate in
\cite{wang2016accelerating} when the objective is convex and Lipschitz smooth.
Moreover, com-SVR-ADMM possesses a rate of $O(1/\sqrt{S})$ when the objective
is convex but without Lipschitz smoothness. We also conduct experiments and
show that it outperforms existing algorithms.