• Faster Rates For Federated Variational Inequalities Faster Rates For Federated Variational Inequalities AuthorsGuanghui Wangâ , Satyen Kale View publication Copy Bibtex In this paper, we study federated optimization for solving stochastic variational inequalities (VIs), a problem that has attracted growing attention in recent years. • Despite substantial progress, a significant gap remains between existing convergence rates and the state-of-the-art bounds known for federated convex optimization. • 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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Guanghui Wang and Satyen Kale present new convergence results for federated optimization of stochastic variational inequalities (VIs). They refine the analysis of the classical Local Extra SGD algorithm, showing tighter guarantees for general smooth, monotone VIs. The authors identify a limitation of Local Extra SGD-excessive client drift-and introduce the Local Inexact Proximal Point Algorithm with Extra Step (LIPPAX). LIPPAX mitigates drift and achieves improved rates in settings with bounded Hessian, bounded operator, and low‑variance noise. The work also extends these results to federated composite VIs, closing a gap between existing rates and state‑of‑the‑art bounds in federated convex optimization.
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