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A non-monotone trust-region method with noisy oracles and additional sampling

Author

Listed:
  • Nataša Krejić

    (University of Novi Sad)

  • Nataša Krklec Jerinkić

    (University of Novi Sad)

  • Ángeles Martínez

    (University of Trieste)

  • Mahsa Yousefi

    (University of Florence
    University of Trieste)

Abstract

In this work, we introduce a novel stochastic second-order method, within the framework of a non-monotone trust-region approach, for solving the unconstrained, nonlinear, and non-convex optimization problems arising in the training of deep neural networks. The proposed algorithm makes use of subsampling strategies that yield noisy approximations of the finite sum objective function and its gradient. We introduce an adaptive sample size strategy based on inexpensive additional sampling to control the resulting approximation error. Depending on the estimated progress of the algorithm, this can yield sample size scenarios ranging from mini-batch to full sample functions. We provide convergence analysis for all possible scenarios and show that the proposed method achieves almost sure convergence under standard assumptions for the trust-region framework. We report numerical experiments showing that the proposed algorithm outperforms its state-of-the-art counterpart in deep neural network training for image classification and regression tasks while requiring a significantly smaller number of gradient evaluations.

Suggested Citation

  • Nataša Krejić & Nataša Krklec Jerinkić & Ángeles Martínez & Mahsa Yousefi, 2024. "A non-monotone trust-region method with noisy oracles and additional sampling," Computational Optimization and Applications, Springer, vol. 89(1), pages 247-278, September.
    • Handle: RePEc:spr:coopap:v:89:y:2024:i:1:d:10.1007_s10589-024-00580-w
    DOI: 10.1007/s10589-024-00580-w
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    References listed on IDEAS

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    1. Johannes Brust & Jennifer B. Erway & Roummel F. Marcia, 2017. "On solving L-SR1 trust-region subproblems," Computational Optimization and Applications, Springer, vol. 66(2), pages 245-266, March.
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