Optimal Rates for Agentic Networked Information Aggregation

TL;DR

The paper establishes the exact optimal rate for information aggregation in a networked learning model where agents pass only predictions. It shows that excess error decays as $O(M^2/D)$ beyond depth $M^2$, and remains constant below it. The results extend to logistic classification under the logit-passing model.

Why It Matters

This resolves a fundamental question about the limits of distributed AI systems where agents share only conclusions. The findings inform the design of scalable, efficient agentic architectures in real-world settings with limited data visibility.

Key Findings

• The excess mean squared error on an $M$-covered path is $O(M^2/D)$ for $D \ge M^2$ and constant for $D < M^2$.
• A tighter lower bound of $\Omega(\sqrt{M/D})$ is established for $D < M^2$ in cyclic instances.
• The same optimal rate holds for logistic classification under the logit-passing model, with convergence matching the regression case up to rescaling.