Proximal Gradient methods with Adaptive Subspace Sampling

Dmitry Grishchenko; Franck Iutzeler; Jérôme Malick

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arXiv · 2004.13356

Proximal Gradient methods with Adaptive Subspace Sampling

Dmitry Grishchenko·Franck Iutzeler·Jérôme Malick

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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; 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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Dmitry Grishchenko, Franck Iutzeler, Jérôme Malick. 2020-04-28. Proximal Gradient methods with Adaptive Subspace Sampling. https://arxiv.org/abs/2004.13356

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