Computable PAC Learning of Continuous Features

Nathanael L. Ackerman, Julian Asilis, Jieqi Di, Cameron E. Freer, Jean-Baptiste Tristan

Abstract: We introduce definitions of computable PAC learning for binary classification over computable metric spaces. We provide sufficient conditions on a hypothesis class to ensure than an empirical risk minimizer (ERM) is computable, and bound the strong Weihrauch degree of an ERM 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.