On Learnability, Complexity and Stability

TL;DR

This paper explores the core concepts of learnability, complexity, and stability in supervised and general learning, reviewing foundational and recent results that connect these ideas.

Contribution

It provides a comprehensive survey of classic and recent results linking learnability, complexity measures, and stability in machine learning theory.

Findings

Learnability is characterized by complexity measures.

Stability of algorithms is crucial for learnability.

Recent results connect stability with learnability in new ways.

Abstract

We consider the fundamental question of learnability of a hypotheses class in the supervised learning setting and in the general learning setting introduced by Vladimir Vapnik. We survey classic results characterizing learnability in term of suitable notions of complexity, as well as more recent results that establish the connection between learnability and stability of a learning algorithm.