# Revisiting Stochastic Extragradient

arXiv: https://arxiv.org/abs/1905.11373 · HTML: https://mlsanity.com/paper/1905.11373/

## Key facts

- Cited by 35 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 May 2019.

## Built on by (most cited first, 30 of 35)

- [Stochastic Variance Reduction for Variational Inequality Methods](https://mlsanity.com/paper/2102.08352/) (2021)
- [Stochastic Gradient Descent-Ascent and Consensus Optimization for Smooth Games: Convergence Analysis under Expected Co-coercivity](https://mlsanity.com/paper/2107.00052/) (2021)
- [Extragradient Method: O(1/K) Last-Iterate Convergence for Monotone Variational Inequalities and Connections With Cocoercivity](https://mlsanity.com/paper/2110.04261/) (2021)
- [Stochastic Gradient Descent-Ascent: Unified Theory and New Efficient Methods](https://mlsanity.com/paper/2202.07262/) (2022)
- [Stochastic Extragradient: General Analysis and Improved Rates](https://mlsanity.com/paper/2111.08611/) (2021)
- [Decentralized Local Stochastic Extra-Gradient for Variational Inequalities](https://mlsanity.com/paper/2106.08315/) (2021)
- [Solving stochastic weak Minty variational inequalities without increasing batch size](https://mlsanity.com/paper/2302.09029/) (2023)
- [On the Convergence of Stochastic Extragradient for Bilinear Games using Restarted Iteration Averaging](https://mlsanity.com/paper/2107.00464/) (2021)
- [Accelerated Primal-Dual Gradient Method for Smooth and Convex-Concave Saddle-Point Problems with Bilinear Coupling](https://mlsanity.com/paper/2112.15199/) (2021)
- [Dealing with unbounded gradients in stochastic saddle-point optimization](https://mlsanity.com/paper/2402.13903/) (2024)
- [Clipped Stochastic Methods for Variational Inequalities with Heavy-Tailed Noise](https://mlsanity.com/paper/2206.01095/) (2022)
- [Single-Call Stochastic Extragradient Methods for Structured Non-monotone Variational Inequalities: Improved Analysis under Weaker Conditions](https://mlsanity.com/paper/2302.14043/) (2023)
- [First Order Methods with Markovian Noise: from Acceleration to Variational Inequalities](https://mlsanity.com/paper/2305.15938/) (2023)
- [Smooth Monotone Stochastic Variational Inequalities and Saddle Point Problems: A Survey](https://mlsanity.com/paper/2208.13592/) (2022)
- [TiAda: A Time-scale Adaptive Algorithm for Nonconvex Minimax Optimization](https://mlsanity.com/paper/2210.17478/) (2022)
- [Stochastic Methods in Variational Inequalities: Ergodicity, Bias and Refinements](https://mlsanity.com/paper/2306.16502/) (2023)
- [Multiplayer Federated Learning: Reaching Equilibrium with Less Communication](https://mlsanity.com/paper/2501.08263/) (2025)
- [Nesterov Finds GRAAL: Optimal and Adaptive Gradient Method for Convex Optimization](https://mlsanity.com/paper/2507.09823/) (2025)
- [Optimal Extragradient-Based Bilinearly-Coupled Saddle-Point Optimization](https://mlsanity.com/paper/2206.08573/) (2022)
- [Variance-Reduced Fast Krasnoselkii-Mann Methods for Finite-Sum Root-Finding Problems](https://mlsanity.com/paper/2406.02413/) (2024)
- [Extragradient Method for (L0, L1)-Lipschitz Root-finding Problems](https://mlsanity.com/paper/2510.22421/) (2025)
- [Unbiased and Biased Variance-Reduced Forward-Reflected-Backward Splitting Methods for Stochastic Composite Inclusions](https://mlsanity.com/paper/2603.15576/) (2026)
- [Recursive Reasoning in Minimax Games: A Level k Gradient Play Method](https://mlsanity.com/paper/2210.16482/) (2022)
- [Diffusion Stochastic Optimization for Min-Max Problems](https://mlsanity.com/paper/2401.14585/) (2024)
- [How to Make the Gradient Mapping Small for Constrained Stochastic Min-Max Problems and Beyond](https://mlsanity.com/paper/2609.08380/) (2026)
- [Training Generative Adversarial Networks with Adaptive Composite Gradient](https://mlsanity.com/paper/2111.05508/) (2021)
- [When is Momentum Extragradient Optimal? A Polynomial-Based Analysis](https://mlsanity.com/paper/2211.04659/) (2022)
- [Forget Sharpness: Perturbed Forgetting of Model Biases Within SAM Dynamics](https://mlsanity.com/paper/2406.06700/) (2024)
- [Shuffling the Data, Stretching the Step-size: Sharper Bias in constant step-size SGD](https://mlsanity.com/paper/2604.10373/) (2026)
- [SARAH-based Variance-reduced Algorithm for Stochastic Finite-sum Cocoercive Variational Inequalities](https://mlsanity.com/paper/2210.05994/) (2022)

## Abstract (arXiv)

We fix a fundamental issue in the stochastic extragradient method by providing a new sampling strategy that is motivated by approximating implicit updates. Since the existing stochastic extragradient algorithm, called Mirror-Prox, of (Juditsky et al., 2011) diverges on a simple bilinear problem when the domain is not bounded, we prove guarantees for solving variational inequality that go beyond existing settings. Furthermore, we illustrate numerically that the proposed variant converges faster than many other methods on bilinear saddle-point problems. We also discuss how extragradient can be applied to training Generative Adversarial Networks (GANs) and how it compares to other methods. Our experiments on GANs demonstrate that the introduced approach may make the training faster in terms of data passes, while its higher iteration complexity makes the advantage smaller.