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Decentralized Online Strongly Convex Optimization with General Compressors and Random Disturbances

Author

Listed:
  • Honglei Liu

    (Nanjing University of Science and Technology)

  • Deming Yuan

    (Nanjing University of Science and Technology)

  • Baoyong Zhang

    (Nanjing University of Science and Technology)

Abstract

This paper considers the decentralized online strongly convex optimization over a multi-agent network, where the objective is to minimize a global loss function accumulated by the local loss functions of all agents. The Time-Varying Scaling Compression method is applied to deal with the communication bottleneck in the presence of disturbances. Then, by using the scaling compression, a decentralized online algorithm is proposed and the convergence results of the algorithm are analyzed. By choosing proper parameters, a sublinear regret can be obtained, which matches the same order as those of algorithms with no disturbances. Finally, numerical simulations are given to demonstrate the efficiency of the proposed algorithm.

Suggested Citation

  • Honglei Liu & Deming Yuan & Baoyong Zhang, 2025. "Decentralized Online Strongly Convex Optimization with General Compressors and Random Disturbances," Journal of Optimization Theory and Applications, Springer, vol. 204(1), pages 1-22, January.
    • Handle: RePEc:spr:joptap:v:204:y:2025:i:1:d:10.1007_s10957-024-02595-z
    DOI: 10.1007/s10957-024-02595-z
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    References listed on IDEAS

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    1. Chuanye Gu & Lin Jiang & Jueyou Li & Zhiyou Wu, 2023. "Privacy-Preserving Dual Stochastic Push-Sum Algorithm for Distributed Constrained Optimization," Journal of Optimization Theory and Applications, Springer, vol. 197(1), pages 22-50, April.
    2. Bin Du & Jiazhen Zhou & Dengfeng Sun, 2020. "Improving the Convergence of Distributed Gradient Descent via Inexact Average Consensus," Journal of Optimization Theory and Applications, Springer, vol. 185(2), pages 504-521, May.
    3. Zhengqing Shi & Chuan Zhou, 2019. "An Improved Distributed Gradient-Push Algorithm for Bandwidth Resource Allocation over Wireless Local Area Network," Journal of Optimization Theory and Applications, Springer, vol. 183(3), pages 1153-1176, December.
    4. Wei Ni & Xiaoli Wang, 2022. "A Multi-Scale Method for Distributed Convex Optimization with Constraints," Journal of Optimization Theory and Applications, Springer, vol. 192(1), pages 379-400, January.
    5. Andrea Simonetto & Hadi Jamali-Rad, 2016. "Primal Recovery from Consensus-Based Dual Decomposition for Distributed Convex Optimization," Journal of Optimization Theory and Applications, Springer, vol. 168(1), pages 172-197, January.
    Full references (including those not matched with items on IDEAS)

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