This work studies algorithms for learning from aggregate responses. We focus
on the construction of aggregation sets (called bags in the literature) for
event-level loss functions. We prove for linear regression and generalized
linear models (GLMs) that the optimal bagging problem reduces to
one-dimensional size-constrained $k$-means clustering. Further, we
theoretically quantify the advantage of using curated bags over random bags. We
then propose the PriorBoost algorithm, which adaptively forms bags of samples
that are increasingly homogeneous with respect to (unobserved) individual
responses to improve model quality. We study label differential privacy for
aggregate learning, and we also provide extensive experiments showing that
PriorBoost regularly achieves optimal model quality for event-level
predictions, in stark contrast to non-adaptive algorithms.

研究聚合反馈学习的算法，重点关注事件级损失函数的聚合集（文献中称为 bags）的构建。理论上证明了对于线性回归和广义线性模型（GLMs），最优的 bagging 问题可以简化为一维受约束的 k 均值聚类问题。进一步地，定量地证明了使用精心选择的聚合集相比于随机聚合集的优势。然后，提出了适应性形成样本聚合集的 PriorBoost 算法，以改善模型质量，聚合集与（未观测到的）个体反馈越来越同质化。研究了用于聚合学习的标签差分隐私，并通过广泛实验表明，PriorBoost 定期实现了事件级预测的最优模型质量，与非适应性算法形成鲜明对比。