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On the asymptotic rate of convergence of Stochastic Newton algorithms and their Weighted Averaged versions

Author

Listed:
  • Claire Boyer

    (Sorbonne-Université
    INRIA)

  • Antoine Godichon-Baggioni

    (Sorbonne-Université)

Abstract

Most machine learning methods can be regarded as the minimization of an unavailable risk function. To optimize the latter, with samples provided in a streaming fashion, we define general (weighted averaged) stochastic Newton algorithms, for which a theoretical analysis of their asymptotic efficiency is conducted. The corresponding implementations are shown not to require the inversion of a Hessian estimate at each iteration under a quite flexible framework that covers the case of linear, logistic or softmax regressions to name a few. Numerical experiments on simulated and real data give the empirical evidence of the pertinence of the proposed methods, which outperform popular competitors particularly in case of bad initializations.

Suggested Citation

  • Claire Boyer & Antoine Godichon-Baggioni, 2023. "On the asymptotic rate of convergence of Stochastic Newton algorithms and their Weighted Averaged versions," Computational Optimization and Applications, Springer, vol. 84(3), pages 921-972, April.
    • Handle: RePEc:spr:coopap:v:84:y:2023:i:3:d:10.1007_s10589-022-00442-3
    DOI: 10.1007/s10589-022-00442-3
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    References listed on IDEAS

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    1. Bolte, Jérôme & Castera, Camille & Pauwels, Edouard & Févotte, Cédric, 2019. "An Inertial Newton Algorithm for Deep Learning," TSE Working Papers 19-1043, Toulouse School of Economics (TSE).
    2. Pelletier, Mariane, 1998. "On the almost sure asymptotic behaviour of stochastic algorithms," Stochastic Processes and their Applications, Elsevier, vol. 78(2), pages 217-244, November.
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