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. Contents1. Introduction 1 1.1. Related work 2 2. Preliminaries 3 2.1. Computable metric spaces and Weihrauch reducibility 3 2.2. Learning theory 6 3. Notions of computable learning theory 8 3.1. Countable hypothesis classes 9 3.2. Examples 10 3.3. Computable learners with noncomputable sample functions 11 4. Computability of learners 12 4.1. Upper bounds 12 4.2. Lower bounds 13 Acknowledgements 16 References 16
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.
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