Halpern Iteration Achieves (epsilon-1/p) p th-Order Oracle Complexity for Monotone Variational Inequalities

arXiv:2608.08463 · math.OC, cs.AI · Submitted 2026-08-09 · Read on arXiv

Lesi Chen, Xinliang Zhang, Hengyu Wang, Chengchang Liu, Yongchao Chen, Jingzhao Zhang

math.OC, cs.AI

Submitted: 2026-08-09

Updated: 2026-08-11

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

Terminology

• Anchored Tensor Method — 7× in this paper
• Generalization — 7× in this paper · explained in 13 episodes
• Regularization — 6× in this paper · explained in 3 episodes
• APEX — 3× in this paper · explained in 1 episode
• Newton Proximal Extragradient — 3× in this paper
• AUC — 2× in this paper · explained in 2 episodes
• Regret — 2× in this paper · explained in 3 episodes
• Adversarial Training — 1× in this paper · explained in 1 episode
• Closed-Loop Control — 1× in this paper · explained in 3 episodes
• Hilbert Space — 1× in this paper · explained in 2 episodes

Sources

• Optimal Methods for Higher-Order Smooth Monotone Variational Inequalities
• Solving Convex-Concave Problems with $\tilde{\mathcal{O}}(\epsilon^{-4/(3p+1)})$ $p$th-Order Oracle Complexity
• High-Order Reduced-Gradient Methods for Composite Variational Inequalities
• Tensor methods for strongly convex strongly concave saddle point problems and strongly monotone variational inequalities
• ODE Analysis of Stochastic Gradient Methods with Optimism and Anchoring for Minimax Problems

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