Fast Stochastic Variance Reduced ADMM for Stochastic Composition Optimization

05/11/2017

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by   Yue Yu, et al.

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We consider the stochastic composition optimization problem proposed in 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( S/S), which improves upon the O(S^-4/9) rate in wang2016accelerating when the objective is convex and Lipschitz smooth. Moreover, com-SVR-ADMM possesses a rate of O(1/√(S)) when the objective is convex but without Lipschitz smoothness. We also conduct experiments and show that it outperforms existing algorithms.