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

2026-09-14

AI Summary

该研究通过使用带有Halpern锚定的随机算法改进了任意时刻算法在解决随机单调变分不等式时的收敛速度，达到O(t^{-1/4})。

Abstract

We analyze a stochastic algorithm with Halpern anchoring for constrained convex-concave problems and monotone variational inequalities. This algorithm is single-loop and single-call since it uses one unbiased sample of the gradient operator at every iteration to be applicable to monotone games with noisy feedback. With $t$ denoting the iteration counter, we prove the anytime last-iterate convergence rate of $O(t^{-1/4})$ for both gradient-mapping norm and restricted gap, improving the best-known rate $O(t^{-1/5})$ that was obtained for the restricted gap function. Our rates cover constrained problems with a potentially unbounded feasible set as well as a structured class of stochastic oracles without a bounded variance.

Problem

• Stochastic Monotone Variational Inequalities
• Last-Iterate Convergence
• Constrained Convex-Concave Problems

Innovation

• Halpern anchoring
• single-loop and single-call algorithm
• stochastic monotone variational inequalities
• anytime last-iterate convergence rate