We consider a weakly supervised learning problem called Learning from Label
Proportions (LLP), where examples are grouped into ``bags'' and only the
average label within each bag is revealed to the learner. We study various
learning rules for LLP that achieve PAC learning guarantees for classification
loss. We establish that the classical Empirical Proportional Risk Minimization
(EPRM) learning rule (Yu et al., 2014) achieves fast rates under realizability,
but EPRM and similar proportion matching learning rules can fail in the
agnostic setting. We also show that (1) a debiased proportional square loss, as
well as (2) a recently proposed EasyLLP learning rule (Busa-Fekete et al.,
2023) both achieve ``optimistic rates'' (Panchenko, 2002); in both the
realizable and agnostic settings, their sample complexity is optimal (up to log
factors) in terms of $\epsilon, \delta$, and VC dimension.

弱监督学习问题中的主题是来自标签比例的学习，研究了多种实现分类损失的标准，包括经典的实证比例风险最小化、去偏差的比例平方损失和最近提出的 EasyLLP 学习规则，这些规则在可实现和不可知设置中均取得了 “乐观速率”，并且在样本复杂度上接近最优（log 因子）。