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Adaptive Sampling Stochastic Multigradient Algorithm for Stochastic Multiobjective Optimization

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Abstract

In this paper, we propose an adaptive sampling stochastic multigradient algorithm for solving stochastic multiobjective optimization problems. Instead of requiring additional storage or computation of full gradients, the proposed method reduces variance by adaptively controlling the sample size used. Without the convexity assumption on the objective functions, we obtain that the proposed algorithm converges to Pareto stationary points in almost surely. We then analyze the convergence rates of the proposed algorithm. Numerical experiments are presented to demonstrate the effectiveness of the proposed algorithm.

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Acknowledgements

The authors are grateful to the editor and two anonymous referees for their valuable comments and constructive suggestions, which have considerably enhanced the quality of the original manuscript. The first author was supported in part by the National Natural Science Foundation of China under grants 12001072 and 12271067, the China Postdoctoral Science Foundation Project under grant 2019M653332, the Chongqing Natural Science Foundation Project under grant CSTB2022NSCQ-MSX1318, the Group Building Scientific Innovation Project for universities in Chongqing under grant CXQT21021 and the open project of Key Laboratory under grant CSSXKFKTQ202006, School of Mathematical Sciences, Chongqing Normal University. The third author was supported in part by the Major Program of the National Natural Science Foundation of China under grants 11991020 and 11991024, the NSFC-RGC (Hong Kong) Joint Research Program under grant 12261160365 and the Chongqing Natural Science Foundation under grant cstc2019jcyj-zdxmX0016.

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Authors and Affiliations

  1. College of Mathematics and Statistics, Chongqing Jiaotong University, Chongqing, 400074, China

    Yong Zhao

  2. College of Mathematics and Statistics, Chongqing University, Chongqing, 401331, China

    Yong Zhao

  3. National Center for Applied Mathematics in Chongqing, Chongqing Normal University, Chongqing, 401331, China

    Wang Chen & Xinmin Yang

  4. School of Mathematical Sciences, Chongqing Normal University, Chongqing, 401331, China

    Xinmin Yang

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  1. Yong Zhao
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Correspondence to Yong Zhao.

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Communicated by René Henrion.

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Zhao, Y., Chen, W. & Yang, X. Adaptive Sampling Stochastic Multigradient Algorithm for Stochastic Multiobjective Optimization. J Optim Theory Appl 200, 215–241 (2024). https://doi.org/10.1007/s10957-023-02334-w

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