Single-loop variance reduction methods in Bregman setups for finite-sum structured variational inequalities

Exploring foci of: arXiv (Cornell University) Single-loop variance reduction methods in Bregman setups for finite-sum structured variational inequalities November 2025 • Zhongbao Wang In this paper, we address variational inequalities (VI) with a finite sum structure by proposing a novel single-loop variance-reduced algorithm that incorporates the Bregman distance. Under the monotone setting, we establish the almost sure convergence of the proposed algorithm and prove that it achieves the optimal complexity of $\mathcal{O}\left(\frac{\sqrt{M}}{\varepsilon }\right)$ for finding an $\varepsilon$-gap. Furthermore, under the non-monotone setting, we derive a complexity of $\mathcal{O}\left(\frac{1}… Open Article Page

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