IDEAS home Printed from https://ideas.repec.org/a/spr/coopap/v84y2023i3d10.1007_s10589-022-00442-3.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10589-022-00442-3
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    File URL: https://libkey.io/10.1007/s10589-022-00442-3?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Pelletier, Mariane, 1999. "An Almost Sure Central Limit Theorem for Stochastic Approximation Algorithms," Journal of Multivariate Analysis, Elsevier, vol. 71(1), pages 76-93, October.
    2. Costa, Manon & Gadat, Sébastien & Bercu, Bernard, 2020. "Stochastic approximation algorithms for superquantiles estimation," TSE Working Papers 20-1142, Toulouse School of Economics (TSE).
    3. Bolte, Jérôme & Le, Tam & Pauwels, Edouard & Silveti-Falls, Antonio, 2022. "Nonsmooth Implicit Differentiation for Machine Learning and Optimization," TSE Working Papers 22-1314, Toulouse School of Economics (TSE).
    4. Samir Adly & Hedy Attouch & Van Nam Vo, 2023. "Convergence of Inertial Dynamics Driven by Sums of Potential and Nonpotential Operators with Implicit Newton-Like Damping," Journal of Optimization Theory and Applications, Springer, vol. 198(1), pages 290-331, July.
    5. Emilie Chouzenoux & Jean-Baptiste Fest, 2022. "SABRINA: A Stochastic Subspace Majorization-Minimization Algorithm," Journal of Optimization Theory and Applications, Springer, vol. 195(3), pages 919-952, December.
    6. Bolte, Jérôme & Pauwels, Edouard, 2019. "Conservative set valued fields, automatic differentiation, stochastic gradient methods and deep learning," TSE Working Papers 19-1044, Toulouse School of Economics (TSE).
    7. Bolte, Jérôme & Glaudin, Lilian & Pauwels, Edouard & Serrurier, Matthieu, 2021. "A Hölderian backtracking method for min-max and min-min problems," TSE Working Papers 21-1243, Toulouse School of Economics (TSE).
    8. Bolte, Jérôme & Pauwels, Edouard, 2021. "A mathematical model for automatic differentiation in machine learning," TSE Working Papers 21-1184, Toulouse School of Economics (TSE).
    9. Yves F. Atchadé, 2006. "An Adaptive Version for the Metropolis Adjusted Langevin Algorithm with a Truncated Drift," Methodology and Computing in Applied Probability, Springer, vol. 8(2), pages 235-254, June.
    10. Koval, Valery & Schwabe, Rainer, 2003. "A law of the iterated logarithm for stochastic approximation procedures in d-dimensional Euclidean space," Stochastic Processes and their Applications, Elsevier, vol. 105(2), pages 299-313, June.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:coopap:v:84:y:2023:i:3:d:10.1007_s10589-022-00442-3. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.