Improving the Last-Iterate Guarantees of Anytime Algorithms for Stochastic Monotone Variational Inequalities
We analyze a stochastic algorithm with Halpern-type anchoring for constrained convex-concave problems and monotone variational inequalities. This single-loop and single-call algorithm 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 an anytime last-iterate convergence rate of $O(t^{-1/4})$ for both the gradient-mapping norm and restricted gap, bypassing the $O(t^{-1/5})$ constrained-anytime bottleneck in the literature. Specializing then to multi-point oracles, we use variance reduction to achieve the $O(t^{-1/2})$ rate with an anytime single-loop algorithm using ...
| Authors | Jun-Hyun Kim, Ahmet Alacaoglu |
|---|---|
| Primary category | math.OC |
| Published | 14 September 2026 |
| Last updated at source | 24 September 2026 |
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