Faster Rates for Federated Variational Inequalities

A paper titled "Faster Rates for Federated Variational Inequalities" by Guanghui Wang and Satyen Kale studies federated optimization for solving stochastic variational inequalities (VIs). According to the paper, a significant gap remains between existing convergence rates for this problem and the state-of-the-art bounds known for federated convex optimization.

The work establishes a series of improved convergence rates. For general smooth and monotone variational inequalities, the authors show that the classical Local Extra SGD algorithm admits tighter guarantees under a refined analysis. The authors then identify an inherent limitation of Local Extra SGD that can lead to excessive client drift.

Motivated by that observation, they propose a new algorithm, the Local Inexact Proximal Point Algorithm with Extra Step (LIPPAX), and report that it mitigates client drift and achieves improved guarantees in several regimes, including bounded Hessian, bounded operator, and low-variance settings.

The results are also extended to federated composite variational inequalities, for which the authors establish improved convergence guarantees. The paper is listed under the Methods and Algorithms research area and is associated with the NeurIPS conference, with a publication date of September 2026. Guanghui Wang is affiliated with the Georgia Institute of Technology, and the work was done while at Apple.