On martingale extensions of Vapnik-Chervonenkis theory with applications to online learning

Abstract

We review recent advances on uniform martingale laws of large numbers and the associated sequential complexity measures. These results may be considered as forming a non-i.i.d. generalization of Vapnik-Chervonenkis theory. We discuss applications to online learning, provide a recipe for designing online learning algorithms, and illustrate the techniques on the problem of online node classification. We outline connections to statistical learning theory and discuss inductive principles of stochastic approximation and empirical risk minimization.