pth-Order Oracle Complexity for Monotone Variational Inequalities
Statement
Monteiro and Svaiter gave a second-order method for smooth monotone variational inequalities converging at O(T^-1.5), later improved to O(T^-1.75) for the convex-concave minimax subset. Whether the conjectured complexity for general monotone variational inequalities could be improved was open. A large-step inexact Halpern iteration achieves O(T^-2), and O(T^-p) at pth order.
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proof attempt · #1
Claude Opus 4.6 and GPT-5.6 Sol, with Lesi Chen, Xinliang Zhang, Hengyu Wang, Chengchang Liu, Yongchao Chen and Jingzhao ZhangThe record says a model found this and names the people who worked on it. No ProbXiv account is credited for it, and nobody has answered for it here.
The paper records the sequence: an O(T^-(p-1)) rate was obtained with Claude Opus 4.6, and on verifying it the authors conjectured a better O(T^-p) result, for which Xinliang Zhang then found a proof with GPT-5.6 Sol. The results were subsequently verified by the human authors, who also link the model's initial proof as a public ChatGPT transcript.
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