Solving Stochastic Variational Inequalities without the Bounded Variance Assumption

• URL: http://arxiv.org/abs/2602.05531v1
• Date: Thu, 05 Feb 2026 10:44:04 GMT
• Title: Solving Stochastic Variational Inequalities without the Bounded Variance Assumption
• Authors: Ahmet Alacaoglu, Jun-Hyun Kim,
• Abstract summary: We analyze algorithms for solving variational inequalities (VI) without the bounded variance or bounded domain assumptions.<n>In our setting, this had been obtained with the bounded complexity assumption as not even satisfied for bi min-max problems with an oracle domain.
• Score: 8.350639529216876
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We analyze algorithms for solving stochastic variational inequalities (VI) without the bounded variance or bounded domain assumptions, where our main focus is min-max optimization with possibly unbounded constraint sets. We focus on two classes of problems: monotone VIs; and structured nonmonotone VIs that admit a solution to the weak Minty VI. The latter assumption allows us to solve structured nonconvex-nonconcave min-max problems. For both classes of VIs, to make the expected residual norm less than $\varepsilon$, we show an oracle complexity of $\widetilde{O}(\varepsilon^{-4})$, which is the best-known for constrained VIs. In our setting, this complexity had been obtained with the bounded variance assumption in the literature, which is not even satisfied for bilinear min-max problems with an unbounded domain. We obtain this complexity for stochastic oracles whose variance can grow as fast as the squared norm of the optimization variable.

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