# Apple — Faster Rates for Federated Variational Inequalities

- Company: Apple (apple.com)
- Announced: 2026-09-28
- Category: research-paper
- Coverage: not counted
- Announcement: yes
- Group: announcements
- Source: https://machinelearning.apple.com/research/federated-variational-inequalities
- Record: https://forck.live/items/14689-faster-rates-for-federated-variational-inequalities
- Subject: Machine Learning Research

Apple researchers present a paper studying federated optimization for stochastic variational inequalities. They provide improved convergence rates for the Local Extra SGD algorithm and propose a new algorithm, LIPPAX, which reduces client drift and achieves better guarantees in bounded Hessian, bounded operator, and low-variance settings. The work also extends results to federated composite variational inequalities.

## Evidence

Verbatim from https://machinelearning.apple.com/research/federated-variational-inequalities:

> In this work, we address this limitation by establishing a series of improved convergence rates. First, we show that, for general smooth and monotone variational inequalities, the classical Local Extra SGD algorithm admits tighter guarantees under a refined analysis. Next, we identify an inherent limitation of Local Extra SGD, which can lead to excessive client drift. Motivated by this observation, we propose a new algorithm, the Local Inexact Proximal Point Algorithm with Extra Step (LIPPAX), and show that it mitigates client drift and achieves improved guarantees in several regimes, including bounded Hessian, bounded operator, and low-variance settings.

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