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Distributed stochastic gradient tracking methods with momentum acceleration for non-convex optimization

Author

Listed:
  • Juan Gao

    (Hebei University of Technology)

  • Xin-Wei Liu

    (Hebei University of Technology)

  • Yu-Hong Dai

    (Chinese Academy of Sciences
    University of Chinese Academy of Sciences)

  • Yakui Huang

    (Hebei University of Technology)

  • Junhua Gu

    (Hebei University of Technology)

Abstract

We consider a distributed non-convex optimization problem of minimizing the sum of all local cost functions over a network of agents. This problem often appears in large-scale distributed machine learning, known as non-convex empirical risk minimization. In this paper, we propose two accelerated algorithms, named DSGT-HB and DSGT-NAG, which combine the distributed stochastic gradient tracking (DSGT) method with momentum accelerated techniques. Under appropriate assumptions, we prove that both algorithms sublinearly converge to a neighborhood of a first-order stationary point of the distributed non-convex optimization. Moreover, we derive the conditions under which DSGT-HB and DSGT-NAG achieve a network-independent linear speedup. Numerical experiments for a distributed non-convex logistic regression problem on real data sets and a deep neural network on the MNIST database show the superiorities of DSGT-HB and DSGT-NAG compared with DSGT.

Suggested Citation

  • Juan Gao & Xin-Wei Liu & Yu-Hong Dai & Yakui Huang & Junhua Gu, 2023. "Distributed stochastic gradient tracking methods with momentum acceleration for non-convex optimization," Computational Optimization and Applications, Springer, vol. 84(2), pages 531-572, March.
    • Handle: RePEc:spr:coopap:v:84:y:2023:i:2:d:10.1007_s10589-022-00432-5
    DOI: 10.1007/s10589-022-00432-5
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    References listed on IDEAS

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    1. Dušan Jakovetić & Nataša Krejić & Nataša Krklec Jerinkić, 2019. "Exact spectral-like gradient method for distributed optimization," Computational Optimization and Applications, Springer, vol. 74(3), pages 703-728, December.
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