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arXiv · 1705.04138

Fast Stochastic Variance Reduced ADMM for Stochastic Composition Optimization

Yue Yu·Longbo Huang
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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.

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Yue Yu, Longbo Huang. 2017-05-11. Fast Stochastic Variance Reduced ADMM for Stochastic Composition Optimization. https://arxiv.org/abs/1705.04138

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