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Accelerated Stochastic Variance Reduction for a Class of Convex Optimization Problems

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Abstract

Katyusha momentum is a famous and efficient alternative acceleration method that used for stochastic optimization problems, which can reduce the potential accumulation error from the process of randomly sampling, induced by classical Nesterov’s acceleration technique. The nature idea behind the Katyusha momentum is to use a convex combination framework instead of extrapolation framework used in Nesterov’s momentum. In this paper, we design a Katyusha-like momentum step, i.e., a negative momentum framework, and incorporate it into the classical variance reduction stochastic gradient algorithm. Based on the built negative momentum-based framework, we proposed an accelerated stochastic algorithm, namely negative momentum-based stochastic variance reduction gradient (NMSVRG) algorithm for minimizing a class of convex finite-sum problems. There is only one extra parameter needed to turn in NMSVRG algorithm, which is obviously more friendly in parameter turning than the original Katyusha momentum-based algorithm. We provided a rigorous theoretical analysis and shown that the proposed NMSVRG algorithm is superior to the SVRG algorithm and is comparable to the best one in the existing literature in convergence rate. Finally, experimental results verify our analysis and show again that our proposed algorithm is superior to the state-of-the-art-related stochastic algorithms.

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Acknowledgements

The authors would like to thank the editor and the anonymous referees for their valuable suggestions and comments which have greatly improved the presentation of this paper. This work is supported in part by the National Nature Science Foundation of China under Grant 61573014, the Fundamental Research Funds for the Central Universities under Grant JB210717 and the Fundamental Research Funds for the Central Universities under Grant YJS2215.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Xi’dian University, Xi’an, 710071, China

    Lulu He & Jimin Ye

  2. College of Mathematics and Physics and Center for Applied Mathematics of Guangxi, Guangxi Minzu University, Nanning, 530006, China

    E. Jianwei

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  1. Lulu He
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  2. Jimin Ye
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  3. E. Jianwei
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Correspondence to Jimin Ye.

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Communicated by Liqun Qi.

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He, L., Ye, J. & Jianwei, E. Accelerated Stochastic Variance Reduction for a Class of Convex Optimization Problems. J Optim Theory Appl 196, 810–828 (2023). https://doi.org/10.1007/s10957-022-02157-1

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