# Forward-backward-forward methods with variance reduction for stochastic variational inequalities

arXiv: https://arxiv.org/abs/1902.03355 · HTML: https://mlsanity.com/paper/1902.03355/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Feb 2019.

## Built on by (most cited first, 5 of 5)

- [Stochastic Variance Reduction for Variational Inequality Methods](https://mlsanity.com/paper/2102.08352/) (2021)
- [On the Convergence of Stochastic Extragradient for Bilinear Games using Restarted Iteration Averaging](https://mlsanity.com/paper/2107.00464/) (2021)
- [Variance-Reduced Fast Krasnoselkii-Mann Methods for Finite-Sum Root-Finding Problems](https://mlsanity.com/paper/2406.02413/) (2024)
- [Unbiased and Biased Variance-Reduced Forward-Reflected-Backward Splitting Methods for Stochastic Composite Inclusions](https://mlsanity.com/paper/2603.15576/) (2026)
- [Stochastic Projective Splitting: Solving Saddle-Point Problems with Multiple Regularizers](https://mlsanity.com/paper/2106.13067/) (2021)

## Abstract (arXiv)

We develop a new stochastic algorithm with variance reduction for solving pseudo-monotone stochastic variational inequalities. Our method builds on Tseng's forward-backward-forward (FBF) algorithm, which is known in the deterministic literature to be a valuable alternative to Korpelevich's extragradient method when solving variational inequalities over a convex and closed set governed by pseudo-monotone, Lipschitz continuous operators. The main computational advantage of Tseng's algorithm is that it relies only on a single projection step and two independent queries of a stochastic oracle. Our algorithm incorporates a variance reduction mechanism and leads to almost sure (a.s.) convergence to an optimal solution. To the best of our knowledge, this is the first stochastic look-ahead algorithm achieving this by using only a single projection at each iteration..