Apple researchers have published a paper addressing convergence rate limitations in federated optimization for solving stochastic variational inequalities (VIs). The study identifies that while progress has been made, a gap persists between existing convergence rates and the state-of-the-art bounds seen in federated convex optimization.
Apple Researchers Propose LIPPAX to Accelerate Federated Variational Inequality Optimization
The researchers first demonstrated that the classical Local Extra Stochastic Gradient Descent (SGD) algorithm allows for tighter guarantees under a refined analysis for general smooth and monotone variational inequalities. However, they also identified an inherent limitation in Local Extra SGD that can result in excessive client drift.
To mitigate this issue, the authors propose a new algorithm called the Local Inexact Proximal Point Algorithm with Extra Step (LIPPAX). Their analysis shows that LIPPAX achieves improved convergence guarantees across several settings, including bounded Hessian, bounded operator, and low-variance environments. The study further extends these results to federated composite variational inequalities.
Sources
- Faster Rates for Federated Variational Inequalities （Apple Machine Learning, 2026-09-28）