This paper contributes to the study of CPAC learnability -- a computable version of PAC learning -- by solving three open questions from recent papers. Firstly, we prove that every improperly CPAC learnable class is contained in a class which is properly CPAC learnable with polynomial sample complexity. This confirms a conjecture by Agarwal et al (COLT 2021). Secondly, we show that there exists a decidable class of hypothesis which is properly CPAC learnable, but only with uncomputably fast growing sample complexity. This solves a question from Sterkenburg (COLT 2022). Finally, we construct a decidable class of finite Littlestone dimension which is not improperly CPAC learnable, strengthening a recent result of Sterkenburg (2022) and answering a question posed by Hasrati and Ben-David (ALT 2023). Together with previous work, our results provide a complete landscape for the learnability problem in the CPAC setting.

翻译：本文致力于研究CPAC可学习性——PAC学习的可计算版本——通过解决近期论文中的三个开放问题。首先，我们证明每个非恰当CPAC可学习的类都包含在一个具有多项式样本复杂度的恰当CPAC可学习类中。这证实了Agarwal等人（COLT 2021）的一个猜想。其次，我们表明存在一个可判定的假设类，它是恰当CPAC可学习的，但其样本复杂度增长快得不可计算。这解决了Sterkenburg（COLT 2022）提出的一个问题。最后，我们构造了一个具有有限Littlestone维数的可判定类，它不是非恰当CPAC可学习的，加强了Sterkenburg（2022）的最新结果，并回答了Hasrati和Ben-David（ALT 2023）提出的一个问题。结合先前的工作，我们的结果为CPAC设定下的可学习性问题提供了完整的前景图。