We study a variant of Collaborative PAC Learning, in which we aim to learn an accurate classifier for each of the $n$ data distributions, while minimizing the number of samples drawn from them in total. Unlike in the usual collaborative learning setup, it is not assumed that there exists a single classifier that is simultaneously accurate for all distributions. We show that, when the data distributions satisfy a weaker realizability assumption, sample-efficient learning is still feasible. We give a learning algorithm based on Empirical Risk Minimization (ERM) on a natural augmentation of the hypothesis class, and the analysis relies on an upper bound on the VC dimension of this augmented class. In terms of the computational efficiency, we show that ERM on the augmented hypothesis class is NP-hard, which gives evidence against the existence of computationally efficient learners in general. On the positive side, for two special cases, we give learners that are both sample- and computationally-efficient.

翻译：我们研究协同PAC学习的一种变体，目标是为$n$个数据分布分别学习一个准确的分类器，同时最小化从这些分布中抽取的总样本数。与通常的协同学习设置不同，此处不假设存在一个同时适用于所有分布的单一分类器。我们证明，当数据分布满足较弱的可实现性假设时，样本高效的学习仍然可行。我们提出了一种基于经验风险最小化（ERM）的学习算法，该算法作用于假设类的自然扩充，其分析依赖于对该扩充类VC维的上界估计。在计算效率方面，我们证明在扩充假设类上的ERM是NP难的，这为一般情形下不存在计算高效的学习器提供了证据。另一方面，针对两种特殊情况，我们给出了兼具样本高效性和计算高效性的学习器。