Consistency of Learning Algorithms Using Attouch–Wets Convergence

In this article, we show that the notion of Tikhonov well-posedness is suitable for studying supervised learning for a wide range of loss functions. We show that supervised learning can be studied from the perspective of variational systems, where one deals with the stability properties of a family of optimization problems. In particular, we prove that the problem of consistency is related to the Attouch-Wets convergence of a sequence of perturbed functionals. Our aim is understanding the potential benefits of applying variational convergence methods to learning theory.