On Learnability, Complexity and Stability

Silvia Villa, Lorenzo Rosasco, Tomaso A. Poggio

Abstract: We considerStability—( Learnability—( the fundamental question of learnability of a hypothesis class in the supervised learningSupervised learning setting and in the general learningGeneral learning setting introduced by Vladimir Vapnik. We survey classic results characterizing learnability in terms of suitable notions of complexity, as well as more recent results that establish the connection between learnability and stability of a learning algorithm.