Nonsmoothness in Machine Learning: specific structure, proximal identification, and applications

Franck Iutzeler (1) , Jérôme Malick (1)

1 DAO - Données, Apprentissage et Optimisation

Nonsmoothness is often a curse for optimization; but it is sometimes a blessing, in particular for applications in machine learning. In this paper, we present the specific structure of nonsmooth optimization problems appearing in machine learning and illustrate how to leverage this structure in practice, for compression, acceleration, or dimension reduction. We pay a special attention to the presentation to make it concise and easily accessible, with both simple examples and general results.

Domaines: Optimisation et contrôle [math.OC]; Traitement du signal et de l'image [eess.SP]; Machine Learning [stat.ML]

Franck Iutzeler, Jérôme Malick. Nonsmoothness in Machine Learning: specific structure, proximal identification, and applications. Set-Valued and Variational Analysis, 2020, 28 (4), pp.661-678. ⟨10.1007/s11228-020-00561-1⟩. ⟨hal-02953985v2⟩