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SABRINA: A Stochastic Subspace Majorization-Minimization Algorithm

Author

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  • Emilie Chouzenoux

    (Université Paris-Saclay)

  • Jean-Baptiste Fest

    (Université Paris-Saclay)

Abstract

A wide class of problems involves the minimization of a coercive and differentiable function F on $${\mathbb {R}}^N$$ R N whose gradient cannot be evaluated in an exact manner. In such context, many existing convergence results from standard gradient-based optimization literature cannot be directly applied and robustness to errors in the gradient is not necessarily guaranteed. This work is dedicated to investigating the convergence of Majorization-Minimization (MM) schemes when stochastic errors affect the gradient terms. We introduce a general stochastic optimization framework, called StochAstic suBspace majoRIzation-miNimization Algorithm SABRINA that encompasses MM quadratic schemes possibly enhanced with a subspace acceleration strategy. New asymptotical results are built for the stochastic process generated by SABRINA. Two sets of numerical experiments in the field of machine learning and image processing are presented to support our theoretical results and illustrate the good performance of SABRINA with respect to state-of-the-art gradient-based stochastic optimization methods.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:195:y:2022:i:3:d:10.1007_s10957-022-02122-y
    DOI: 10.1007/s10957-022-02122-y
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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. Jérôme Bolte & Edouard Pauwels, 2016. "Majorization-Minimization Procedures and Convergence of SQP Methods for Semi-Algebraic and Tame Programs," Mathematics of Operations Research, INFORMS, vol. 41(2), pages 442-465, May.
    3. Nicolas Loizou & Peter Richtárik, 2020. "Momentum and stochastic momentum for stochastic gradient, Newton, proximal point and subspace descent methods," Computational Optimization and Applications, Springer, vol. 77(3), pages 653-710, December.
    4. Gadat, Sébastien & Gavra, Ioana, 2021. "Asymptotic study of stochastic adaptive algorithm in non-convex landscape," TSE Working Papers 21-1175, Toulouse School of Economics (TSE).
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