On computable learning of continuous features

TL;DR

This paper explores the computability aspects of PAC learning for continuous features, establishing conditions for computable learners and analyzing their computational complexity within metric spaces.

Contribution

It introduces computable PAC learning definitions for metric spaces and analyzes the computability and limitations of empirical risk minimizers.

Findings

Provided sufficient conditions for computable ERM learners.

Bound the Weihrauch degree of ERM learners under general conditions.

Demonstrated a PAC learnable class without any proper computable PAC learner.

Abstract

We introduce definitions of computable PAC learning for binary classification over computable metric spaces. We provide sufficient conditions for learners that are empirical risk minimizers (ERM) to be computable, and bound the strong Weihrauch degree of an ERM learner under more general conditions. We also give a presentation of a hypothesis class that does not admit any proper computable PAC learner with computable sample function, despite the underlying class being PAC learnable.