Optimal Rates for Agentic Networked Information Aggregation

TL;DR - This paper establishes optimal error rates for networked learning paths where agents observe partial features and pass only their predictions forward. It shows that excess error remains constant until depth (M^2), then decays at the tight rate (\Theta(M^2/D)).

• Closes the gap between the previous (O(M/\sqrt D)) upper bound and weaker lower bounds for (M)-covered paths.
• Constructs instances yielding constant excess error for (D<M^2) and (\Omega(M^2/D)) for (D\ge M^2).
• Proves geometric error contraction for any fixed distribution, so no single instance can sustain a polynomial lower bound at every depth.
• Extends the optimal rate to logistic classification with binary cross-entropy by relating logit-passing paths to rescaled least-squares paths.