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Journal Articles Mathematics of Operations Research Year : 2021

Proximal Gradient methods with Adaptive Subspace Sampling


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; ii) an identification-based sampling of the subspaces. Their interplay brings a significant performance improvement on typical learning problems in terms of dimensions explored.
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Dates and versions

hal-02555292 , version 1 (27-04-2020)
hal-02555292 , version 2 (03-11-2020)



Dmitry Grishchenko, Franck Iutzeler, Jérôme Malick. Proximal Gradient methods with Adaptive Subspace Sampling. Mathematics of Operations Research, 2021, 46 (4), pp.1235-1657, C2. ⟨10.1287/moor.2020.1092⟩. ⟨hal-02555292v2⟩
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