发表机构
Google Research; University of California, Irvine; University of Maryland（谷歌研究院; 加州大学尔湾分校; 马里兰大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究智能体网络信息聚合的最优设计，证明单父节点无法保证精确聚合，而双父节点在深度O(d log d)内可实现，且深度和智能体数量均达到最优。
AI 中文摘要
我们研究了Kearns、Roth和Ryu（SODA 2026）引入的网络化学习模型中的信息聚合问题。存在一个关于$d$个特征的固定分布和一个共同标签。智能体在有向无环图上按拓扑顺序学习。每个智能体观察一部分特征及其父节点的预测，拟合一个线性预测器以最小化均方误差，并且仅将其预测传递给后继。全局预测器是使用所有特征的最佳线性预测器。Kearns、Roth和Ryu表明，在具有适当特征覆盖的足够深路径上，输出智能体的误差趋近于全局预测器的误差，而深度不足即使在大型网络中也可能阻碍聚合。与他们对给定图和特征分配的主要关注点不同，我们考虑模型在两种设置下的极限。在自适应设计者设置中，设计者在已知分布的情况下选择图、特征分配和输出智能体。在不知情设计者设置中，设计者在对手选择分布之前固定三者。每个智能体观察一个特征，并从有限数量的父节点接收预测。当输出智能体与全局预测器完全匹配时，我们称聚合是精确的。对于$d\ge3$，我们证明即使设计者知道分布，当每个智能体只有一个父节点时，没有有限深度能保证对所有分布进行精确聚合。相反，每个智能体有两个父节点即使在不知情设计者设置中也足以实现精确聚合。一个固定的图、特征分配和输出智能体在深度$O(d\log d)$下对所有分布实现这一点。知道分布可将深度减少到$O(d)$。两种构造都使用$O(d^2)$个智能体，对于两个父节点的情况常数非常大。我们证明深度和智能体数量的界限在常数因子内都是最优的。
英文摘要
We study information aggregation in the networked learning model introduced by Kearns, Roth, and Ryu (SODA 2026). There is a fixed distribution over $d$ features and a common label. Agents learn in topological order on a directed acyclic graph. Each observes a subset of the features and its parents' predictions, fits a linear predictor to minimize mean squared error, and passes only its prediction forward. The global predictor is the best linear predictor using all features. Kearns, Roth, and Ryu show that the output agent's error approaches the global predictor's error along sufficiently deep paths with suitable feature coverage, while insufficient depth can prevent aggregation even in large networks. In contrast to their main focus on a given graph and feature allocation, we consider the limits of the model under two settings. In the adaptive designer setting, a designer chooses the graph, feature allocation, and output agent knowing the distribution. In the oblivious designer setting, the designer fixes all three before an adversary chooses the distribution. Each agent observes one feature and receives predictions from a limited number of parents. We call the aggregation exact when the output agent matches the global predictor exactly. For $d\ge3$, we show that no finite depth guarantees exact aggregation for every distribution with one parent per agent, even when the designer knows the distribution. In contrast, two parents per agent suffice for exact aggregation even in the oblivious designer setting. A fixed graph, feature allocation, and output agent achieve this for every distribution at depth $O(d\log d)$. Knowing the distribution reduces the depth to $O(d)$. Both constructions use $O(d^2)$ agents, with a very large constant for two parents. We show the bounds on the depth and number of agents are all optimal up to constant factors.
