The sample complexity of multi-group learning is shown to improve in the group-realizable setting over the agnostic setting, even when the family of groups is infinite so long as it has finite VC dimension. The improved sample complexity is obtained by empirical risk minimization over the class of group-realizable concepts, which itself could have infinite VC dimension. Implementing this approach is also shown to be computationally intractable, and an alternative approach is suggested based on improper learning.

翻译：研究表明，在群可实现的设定下，即使群族是无限的（只要其具有有限的VC维），多群组学习的样本复杂度相较于不可知设定也有所改善。这一改进的样本复杂度是通过在群可实现概念类上进行经验风险最小化获得的，而该类本身可能具有无限的VC维。同时，研究也表明实现这一方法在计算上是不可行的，并基于非恰当学习提出了一种替代方案。