发表机构
Amazon; Amazon Responsible AI（亚马逊; 亚马逊负责任人工智能部门）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对Kearns等人2026年提出的网络化信息聚合问题中MSE上下界存在的研究空白，该研究利用预测器结构不变性，将下界结论推广至满足正则条件的凸损失函数，成功闭合了相关研究的误差界差距。
AI 中文摘要
网络化信息聚合问题由Kearns等人（2026）研究，该问题涉及一组位于有向无环图$G$顶点上的学习者，每个学习者可访问局部特征及其父节点学习到的预测器，用于为固定随机变量$Y$学习线性预测器$\widehat Y\\
英文摘要
The problem of networked information aggregation, studied in Kearns et al. (2026), involves a group of learners situated on the vertices of a directed acyclic graph $G$, each learning a linear predictor $\widehat Y$ for a fixed random variable $Y$ given access to a local feature, as well as the predictors learnt by its parents. Learning proceeds iteratively, with learners ordered according to a topological sort of $G$. The main quantity of interest is the error incurred by the current learner, constrained to this flow of information, with respect to the best linear predictor using all the features seen so far. When the studied error is the MSE, i.e., $\mathbb{E} (\widehat Y - Y)^2$, Kearns et al. (2026) show that the error is at most $O(1/\sqrt{D})$ along a path of length $D$. They also obtain a hard instance where the MSE is lower bounded by $Ω(1/D)$, leaving the correct order open. In this work, we resolve this central open problem, and obtain a family of worst case problem instances with a MSE lower bound of $Ω(1/\sqrt{D})$. By exploiting invariances in the structure of the learnt predictors, our analysis generalizes to all convex loss functions $\ell(\widehat Y, Y)$ satisfying regularity conditions which include strong convexity in a ball around the origin, and that the ideal predictor minimizing the population loss is positively correlated with the label. We show that networked information aggregation on a gaussian instance in our worst case family incurs an $\ell$-error lower bounded by $Ω(1/\sqrt{D})$ with respect to this ideal predictor. We demonstrate that a variety of common losses satisfy these regularity conditions. In particular, the logistic loss satisfies them, and hence our analysis also closes the gap between the upper and lower bounds in Bateni et al. (2026).
