Optimal Rates for Agentic Networked Information Aggregation

Based on the pioneering work by Kearns, Roth, and Ryu (SODA’26), the latest research analyzes information aggregation problems in network learning models that simulate agent-based AI patterns. The model assumes that each agent only observes part of the data and conveys conclusions, using a mean squared error loss function. The study revised the original convergence bounds: when the network depth is less than M², the correct convergence rate for excess mean squared error is constant; when the depth is greater than or equal to M², the correct convergence rate is Θ(M²/D). Additionally, the study improved the lower bound for cyclic instances to Ω(√M/D) and demonstrated that under any fixed distribution, excess error decreases geometrically along the path, thereby ruling out the possibility of a polynomial lower bound for all depths due to a single instance. Furthermore, this optimal convergence rate conclusion has been extended to the log-transmission model proposed by Bateni et al., including the case of logistic regression.