How to Make the Gradient Mapping Small for Constrained Stochastic Min-Max Problems and Beyond
We study the stochastic first-order oracle complexity for constrained or regularized convex-concave min-max optimization and stochastic monotone variational inequalities. We focus on the case when suboptimality is measured in terms of the gradient mapping, also known as, forward-backward or natural residual, an optimality notion that generalizes the gradient norm for unconstrained problems. In this setting, under standard unbiased oracle access with now-standard variance assumptions, the best-known complexity for making the norm of the gradient mapping less than $\varepsilon$ is $\widetilde{O}(\varepsilon^{-4})$, compared to the near-optimal $\widetilde{O}(\varepsilon^{-2})$ that is estab...
| Authors | Ahmet Alacaoglu |
|---|---|
| Primary category | math.OC |
| Published | 8 September 2026 |
| Last updated at source | 8 September 2026 |
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