Blumer et al. (1987, 1989) showed that any concept class that is learnable by Occam algorithms is PAC learnable. Board and Pitt (1990) showed a partial converse of this theorem: for concept classes that are closed under exception lists, any class that is PAC learnable is learnable by an Occam algorithm. However, their Occam algorithm outputs a hypothesis whose complexity is $\delta$-dependent, which is an important limitation. In this paper, we show that their partial converse applies to Occam algorithms with $\delta$-independent complexities as well. Thus, we provide a posteriori justification of various theoretical results and algorithm design methods which use the partial converse as a basis for their work.

翻译：Blumer等人（1987, 1989）表明，任何可由奥卡姆算法学习的概念类都是PAC可学习的。Board和Pitt（1990）证明了该定理的部分逆命题：对于在例外列表下封闭的概念类，任何PAC可学习的类均可通过奥卡姆算法学习。然而，他们的奥卡姆算法输出的假设复杂度依赖于$\delta$，这一局限性至关重要。本文证明，该部分逆命题同样适用于复杂度不依赖于$\delta$的奥卡姆算法。因此，我们为诸多以该部分逆命题为基础的理论结果与算法设计方法提供了后验合理性证明。