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Proximal Gradient Methods with Adaptive Subspace Sampling

Author

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  • Dmitry Grishchenko

    (Laboratoire Jean Kuntzmann, Université Grenoble Alpes, 38402 Saint-Martin-d’Heres, France; Laboratoire d’Informatique de Grenoble, Université Grenoble Alpes, 38401 Saint-Martin-d’Heres, France)

  • Franck Iutzeler

    (Laboratoire Jean Kuntzmann, Université Grenoble Alpes, 38402 Saint-Martin-d’Heres, France)

  • Jérôme Malick

    (Laboratoire Jean Kuntzmann, Université Grenoble Alpes, 38402 Saint-Martin-d’Heres, France; Centre National de la Recherche Scientifique, 75016 Paris, France)

Abstract

Many applications in machine learning or signal processing involve nonsmooth optimization problems. This nonsmoothness brings a low-dimensional structure to the optimal solutions. In this paper, we propose a randomized proximal gradient method harnessing this underlying structure. We introduce two key components: (i) a random subspace proximal gradient algorithm; and (ii) an identification-based sampling of the subspaces. Their interplay brings a significant performance improvement on typical learning problems in terms of dimensions explored.

Suggested Citation

  • Dmitry Grishchenko & Franck Iutzeler & Jérôme Malick, 2021. "Proximal Gradient Methods with Adaptive Subspace Sampling," Mathematics of Operations Research, INFORMS, vol. 46(4), pages 1303-1323, November.
    • Handle: RePEc:inm:ormoor:v:46:y:2021:i:4:p:1303-1323
    DOI: 10.1287/moor.2020.1092
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