On empirical risk minimization and its variants for statistical learning

In this talk, we review fundamental principles of empirical risk minimization and its performance guarantees for statistical learning. We discuss the close interaction with the field of empirical processes and the connection to Vapnik–Chervonenkis combinatorics (including the notion of combinatorial dimension). We present the best known theoretical guarantees for the prediction error of empirical risk minimizers, discuss the limitations of the method, and mention some recent contributions.