Fast Stochastic Variance Reduced ADMM for Stochastic Composition Optimization
This addresses optimization challenges in machine learning and statistics, offering incremental improvements in convergence rates for stochastic composition problems.
The paper tackles the stochastic composition optimization problem by proposing the first ADMM-based algorithm, com-SVR-ADMM, which achieves linear convergence for strongly convex objectives and improves convergence rates to O(log S/S) for convex cases, outperforming existing methods in experiments.
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.