Paper tightens convergence rates for federated variational inequalities and proposes LIPPAX
The paper refines analysis of Local Extra SGD to obtain tighter convergence guarantees for smooth monotone federated variational inequalities, identifies an inherent client-drift limitation of that method, and introduces a new algorithm — Local Inexact Proximal Point Algorithm with Extra Step (LIPPAX) — which provably mitigates drift and yields improved convergence rates in regimes such as bounded Hessian, bounded operator, and low-variance; results are also extended to federated composite variational inequalities.