# Optimal Rates for Agentic Networked Information Aggregation

arXiv: https://arxiv.org/abs/2609.05318 · HTML: https://mlsanity.com/paper/2609.05318/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in General LLM agent frameworks and benchmarks, one of 16 directions in LLM agents and tool use.
- Builds on 12 of its 28 references that are in the map.
- First posted on arXiv 4 Sep 2026.

## Placed in

- LLM agents and tool use / [General LLM agent frameworks and benchmarks](https://mlsanity.com/agents/general-llm-agent-frameworks-and-benchmarks/)

## Builds on (most cited first, 12 of 12)

- [Large Language Model based Multi-Agents: A Survey of Progress and Challenges](https://mlsanity.com/paper/2402.01680/) (2024)
- [Split learning for health: Distributed deep learning without sharing raw patient data](https://mlsanity.com/paper/1812.00564/) (2018)
- [Multiaccuracy: Black-Box Post-Processing for Fairness in Classification](https://mlsanity.com/paper/1805.12317/) (2018)
- [SecureBoost: A Lossless Federated Learning Framework](https://mlsanity.com/paper/1901.08755/) (2019)
- [Loss Minimization through the Lens of Outcome Indistinguishability](https://mlsanity.com/paper/2210.08649/) (2022)
- [Collaborative Prediction: Tractable Information Aggregation via Agreement](https://mlsanity.com/paper/2504.06075/) (2025)
- [Tractable Agreement Protocols](https://mlsanity.com/paper/2411.19791/) (2024)
- [Networked Information Aggregation via Machine Learning](https://mlsanity.com/paper/2507.09683/) (2025)
- [Networked Information Aggregation for Binary Classification](https://mlsanity.com/paper/2605.01082/) (2026)
- [Optimal Deterministic Multicalibration and Omniprediction](https://mlsanity.com/paper/2606.20557/) (2026)
- [Communication Lower Bounds for Distributed Convex Optimization: Partition Data on Features](https://mlsanity.com/paper/1612.00599/) (2016)
- [Model Agreement via Anchoring](https://mlsanity.com/paper/2602.23360/) (2026)

## Built on by (most cited first, 1 of 1)

- [Optimal Networks for Agentic Information Aggregation](https://mlsanity.com/paper/2609.35537/) (2026)

## Abstract (arXiv)

Building on the pioneering paper of Kearns, Roth, and Ryu (SODA'26), we study information aggregation in a networked learning model. The model captures a central pattern in agentic AI: each agent sees only part of the data and passes on only its own conclusion. Their model considers a linear regression problem with the mean squared error (MSE) loss. Agents sit in a DAG and each sees only a subset of the features and its parents' predictions, fits a linear predictor, and passes only its prediction forward. The benchmark is the full-feature learner that sees all raw features. A path of depth D is M-covered if every block of M consecutive agents collectively sees all raw features. Kearns, Roth, and Ryu proved that the excess mean squared error of the last agent on such a path is O(M/√ D), and gave a cyclic instance with excess error Omega(M/D) for D<M2. We close this gap: the correct rate is constant up to depth M2, and Theta(M2/D) beyond it. We first give a sharper analysis of the cyclic instance and improve its lower bound to Omega(√M/D) for D<M2. We then construct, for every depth D≥ M2, an M-covered path of depth D with excess error Omega(M2/D). The same instance gives the constant lower bound for all D < M2. We also show that for any fixed distribution the excess error contracts geometrically along the path, ruling out any single instance that witnesses any polynomial lower bound at every depth. Finally, we prove the same optimal rate for logistic classification in the logit-passing model of Bateni et al., which considers the binary cross-entropy (BCE) loss. The same improved upper bound of O(M2/D) holds, and we transfer all the regression lower bounds by showing that on those examples the logistic path follows the least-squares path up to rescaling.