Iterative regularization in classification via hinge loss diagonal descent

Estimating a quantity of interest from finite measurements is a central problem in a number of fields including machine learning but also statistics and signal processing. In this context, a key idea is that reliable estimation requires imposing some prior assumptions on the problem at hand. The theory of inverse problems provides a principled framework to formalize this idea [27]. The quantity of interest is typically seen as a function, or a vector, and prior assumptions take the form of suitable functionals, called regularizers. Following this idea, Tikhonov regularization provides a classic approach to estimate solutions [83, 84]. Indeed, the latter are found by minimizing an empirical objective where a data fit term is penalized adding the chosen regularizer. Other regularization approaches are classic in inverse problems, and in particular iterative regularization has become popular in machine learning, see e.g.