GOMA Achieves First Stochastic Convergence Guarantee for Variational Inequalities

The paper introduces GOMA, a family of first-order methods for monotone variational inequalities. In the stochastic setting with unbounded variance, a simplified variant of GOMA achieves an O(1/\sqrt{k}) last-iterate convergence rate on the squared gradient norm, without variance reduction or growing batches. This is the first such guarantee for unconstrained stochastic monotone Lipschitz variational inequalities.