Optimal Lower Bounds for Networked Information Aggregation

Sicherheitsmeldung mit Schweregrad noch nicht bewertet. Technische Details im Tab „Originaltext“; empfohlene Schritte in der Checkliste.

Originaltext der Quelle (nicht übersetzt) – die deutsche Zusammenfassung findest du im Tab „Kurzfassung".

arXiv:2608.15472v1 Announce Type: cross Abstract: The problem of networked information aggregation, studied in Kearns et al. (2026), involves a group of learners situated on the vertices of a directed acyclic graph $G$, each learning a linear predictor $\widehat Y$ for a fixed random variable $Y$ given access to a local feature, as well as the predictors learnt by its parents. Learning proceeds iteratively, with learners ordered according to a topological sort of $G$. The main quantity of interest is the error incurred by the current learner, constrained to this flow of information, with respect to the best linear predictor using all the features seen so far. When the studied error is the MSE, i.e., $\mathbb{E} (\widehat Y - Y)^2$, Kearns et al. (2026) show that the error is at most $O(1/\sqrt{D})$ along a path of length $D$. They also obtain a hard instance where the MSE is lower bounded by $\Omega(1/D)$, leaving the correct order open. In this work, we resolve this central open problem, and obtain a family of worst case problem instances with a MSE lower bound of $\Omega(1/\sqrt{D})$. By exploiting invariances in the structure of the learnt predictors, our analysis generalizes to all convex loss functions $\ell(\widehat Y, Y)$ satisfying regularity conditions which include strong convexity in a ball around the origin, and that the ideal predictor minimizing the population loss is positively correlated with the label. We show that networked information aggregation on a gaussian instance in our worst case family incurs an $\ell$-error lower bounded by …

Vollständiger Originalartikel ↗

• Betroffenheit im eigenen Stack prüfen: Versionen/Komponenten abgleichen.
• Originalquelle / Hersteller-Advisory lesen: https://arxiv.org/abs/2608.15472
• Verfügbaren Patch oder Workaround einspielen und dokumentieren.