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.

翻译：我们引入了可计算PAC学习比可计算指标空间的二进制分类定义。 我们为作为经验风险最小化(ERM)学习者的学习者提供了足够的可计算条件,并将机构风险管理学习者的威赫拉赫程度约束在更一般的条件下。 我们还介绍了一个假设类别,该类别不承认任何具有可计算抽样功能的可计算PAC学习者,尽管基础类别为PAC可以学习。