Realizable Learning is All You Need

TL;DR

This paper introduces a simple, unified framework demonstrating the fundamental equivalence between realizable and agnostic learnability across diverse learning models, extending to broader properties like noise tolerance and privacy.

Contribution

It provides the first model-independent reduction that unifies and extends the understanding of realizable and agnostic learnability in various settings.

Findings

Unified framework applies to models with no known learnability characterization

Extends equivalence to robust, partial, fair learning, and statistical query models

Highlights property generalization as a broader phenomenon

Abstract

The equivalence of realizable and agnostic learnability is a fundamental phenomenon in learning theory. With variants ranging from classical settings like PAC learning and regression to recent trends such as adversarially robust learning, it's surprising that we still lack a unified theory; traditional proofs of the equivalence tend to be disparate, and rely on strong model-specific assumptions like uniform convergence and sample compression. In this work, we give the first model-independent framework explaining the equivalence of realizable and agnostic learnability: a three-line blackbox reduction that simplifies, unifies, and extends our understanding across a wide variety of settings. This includes models with no known characterization of learnability such as learning with arbitrary distributional assumptions and more general loss functions, as well as a host of other popular settings such as robust learning, partial learning, fair learning, and the statistical query model. More generally, we argue that the equivalence of realizable and agnostic learning is actually a special case of a broader phenomenon we call property generalization: any desirable property of a learning algorithm (e.g. noise tolerance, privacy, stability) that can be satisfied over finite hypothesis classes extends (possibly in some variation) to any learnable hypothesis class.