Home » Publication » 27081

Dettaglio pubblicazione

2018, MATHEMATICAL PROGRAMMING, Pages 99-127 (volume: 167)

Consistent learning by composite proximal thresholding (01a Articolo in rivista)

Combettes Patrick L., Salzo Saverio, Villa Silvia

We investigate the modeling and the numerical solution of machine learning problems with prediction functions which are linear combinations of elements of a possibly infinite dictionary of functions. We propose a novel flexible composite regularization model, which makes it possible to incorporate various priors on the coefficients of the prediction function, including sparsity and hard constraints. We show that the estimators obtained by minimizing the regularized empirical risk are consistent in a statistical sense, and we design an error-tolerant composite proximal thresholding algorithm for computing such estimators. New results on the asymptotic behavior of the proximal forward–backward splitting method are derived and exploited to establish the convergence properties of the proposed algorithm. In particular, our method features a o(1 / m) convergence rate in objective values.
Gruppo di ricerca: Continuous Optimization
© Università degli Studi di Roma "La Sapienza" - Piazzale Aldo Moro 5, 00185 Roma