Near-Optimal Pure Single-Loop Extragradient Method for Strongly Convex--Strongly Concave Minimax Optimization

arXiv:2609.20327v1 Announce Type: cross Abstract: We study smooth strongly convex--strongly concave minimax optimization with general nonlinear coupling in the deterministic unconstrained setting. We propose a pure single-loop damped extragradient method with fixed parameters and two new full-gradient evaluations per iteration after one initialization query. The method uses an auxiliary feedback recursion and requires no inner solves, accuracy schedules, or staged restarts. We establish last-iterate linear convergence and show that reducing the squared Euclidean distance to the saddle point to an arepsilon fraction of its initial value requires O(sqrt{kappa_xkappa_y}log(2kappa_xkappa_y/arepsilon)) full-gradient queries, where kappa_x=L/mu_x and kappa_y=L/mu_y. This bound attains the optimal condition-number order up to logarithmic factors through fixed explicit updates. Numerical experiments demonstrate the effectiveness of the method.

Source: arXiv cs.LG | 2026-09-18