Improving the Last-Iterate Guarantees of Anytime Algorithms for Stochastic Monotone Variational Inequalities

arXiv:2609.15257 · math.OC, cs.LG · Submitted 2026-09-14 · Read on arXiv

math.OC, cs.LG

Submitted: 2026-09-14

Updated: 2026-09-24

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Regret — 7× in this paper · explained in 3 episodes
• Anytime Last-Iterate Convergence — 2× in this paper · explained in 1 episode
• Adaptivity — 1× in this paper · explained in 1 episode
• Loss Function — 1× in this paper · explained in 2 episodes
• Sample Complexity — 1× in this paper · explained in 15 episodes

Sources

• How to Make the Gradient Mapping Small for Constrained Stochastic Min-Max Problems and Beyond
• Towards Weaker Variance Assumptions for Stochastic Optimization
• Last-Iterate Convergence of Anchored Gradient Descent
• Unbiased and Biased Variance-Reduced Forward-Reflected-Backward Splitting Methods for Stochastic Composite Inclusions
• Last-Iterate Convergence of Single-Loop Stochastic Methods for Constrained Convex-Concave Minimax Problems

Related papers

• Lions and Muons: Optimization via Stochastic Frank-Wolfe under Heavy-Tailed Noise
• Adam-HNAG: A Convergent Reformulation of Adam with Accelerated Rate
• Incremental Learning in Mirror Flows
• Online Control via Counterfactual Tracking
• Asynchronous Replanning in Two Population Linear Quadratic Mean Field Games: Information Requirements and Stability
• Petrov-Galerkin operator inference with application to stability-encouraging identification