One-Shot Federated Ridge Regression Eliminates Iterative Communication Overhead

Global: One-Shot Federated Ridge Regression Eliminates Iterative Communication Overhead

Researchers presenting a new federated learning protocol on arXiv have demonstrated that distributed linear regression can be solved without iterative communication between clients and a central server. The method, described in a paper posted in January 2026, aggregates each client’s Gram matrix and moment vector a single time, allowing the server to reconstruct the exact ridge regression solution under a coverage condition. By transmitting sufficient statistics only once, the approach reduces communication load and improves differential‑privacy guarantees.

Method Overview

The authors formulate federated ridge regression as a distributed equilibrium problem. Each participating client computes local sufficient statistics—the Gram matrix of its features and the corresponding response vector—and sends these to the server in a single round. The server then performs a matrix inversion to obtain the global ridge solution, eliminating the need for repeated gradient exchanges typical of FedAvg and related algorithms.

Theoretical Guarantees

According to the arXiv preprint, the authors prove exact recovery of the centralized ridge estimator when the aggregated client feature matrices satisfy a specific coverage condition. For heterogeneous data that violate this condition, the paper provides non‑asymptotic error bounds that depend on the spectral properties of the combined Gram matrix.

Communication Efficiency

Traditional iterative methods require communication on the order of O(Rd), where R is the number of rounds and d the feature dimension. The proposed one‑shot approach reduces total communication to O(d²), and for high‑dimensional settings the authors introduce random projection techniques that lower the cost further to O(m²), with m ≪ d.

Privacy Implications

Because noise is injected only once per client, the protocol avoids the composition penalty that degrades privacy in multi‑round schemes. The authors claim that this yields stronger differential‑privacy guarantees while maintaining model accuracy.

Experimental Validation

Comprehensive experiments on synthetic heterogeneous regression tasks show that the one‑shot method matches the accuracy of FedAvg while using up to 38 times less communication. The paper also reports robustness to client dropout and presents a federated cross‑validation procedure for hyper‑parameter selection.

Limitations and Future Work

The authors note that the framework extends naturally to kernel methods and random‑feature models but does not apply to general nonlinear architectures. Future research directions include adapting the approach to deep learning models and exploring adaptive projection schemes.

This report is based on information from arXiv, licensed under Academic Preprint / Open Access. Based on the abstract of the research paper. Full text available via ArXiv.