# Properties of Fixed Points of Generalised Extra Gradient Methods Applied to Min-Max Problems

arXiv: https://arxiv.org/abs/2504.03069 · HTML: https://mlsanity.com/paper/2504.03069/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 29 references that are in the map.
- First posted on arXiv 3 Apr 2025.

## Builds on (most cited first, 9 of 9)

- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [Deep Decentralized Multi-task Multi-Agent Reinforcement Learning under Partial Observability](https://mlsanity.com/paper/1703.06182/) (2017)
- [The Limit Points of (Optimistic) Gradient Descent in Min-Max Optimization](https://mlsanity.com/paper/1807.03907/) (2018)
- [Efficient Methods for Structured Nonconvex-Nonconcave Min-Max Optimization](https://mlsanity.com/paper/2011.00364/) (2020)
- [Last-iterate Convergence of Decentralized Optimistic Gradient Descent/Ascent in Infinite-horizon Competitive Markov Games](https://mlsanity.com/paper/2102.04540/) (2021)
- [The limits of min-max optimization algorithms: convergence to spurious non-critical sets](https://mlsanity.com/paper/2006.09065/) (2020)
- [Stochastic Gradient Descent-Ascent: Unified Theory and New Efficient Methods](https://mlsanity.com/paper/2202.07262/) (2022)
- [Direct-Search for a Class of Stochastic Min-Max Problems](https://mlsanity.com/paper/2102.11386/) (2021)
- [Two-timescale Extragradient for Finding Local Minimax Points](https://mlsanity.com/paper/2305.16242/) (2023)

## Built on by (most cited first, 3 of 3)

- [Solving the Offline and Online Min-Max Problem of Non-smooth Submodular-Concave Functions: A Zeroth-Order Approach](https://mlsanity.com/paper/2601.21243/) (2026)
- [On the Stability Connection Between Discrete-Time Algorithms and Their Resolution ODEs: Applications to Min-Max Optimisation](https://mlsanity.com/paper/2603.01430/) (2026)
- [From Cursed to Competitive: Closing the ZO-FO Gap via Input-to-State Stability](https://mlsanity.com/paper/2604.25372/) (2026)

## Abstract (arXiv)

This paper studies properties of fixed points of generalised Extra-gradient (GEG) algorithms applied to min-max problems. We discuss connections between saddle points of the objective function of the min-max problem and GEG fixed points. We show that, under appropriate step-size selections, the set of saddle points (Nash equilibria) is a subset of stable fixed points of GEG. Convergence properties of the GEG algorithm are obtained through a stability analysis of a discrete-time dynamical system. The results and benefits when compared to existing methods are illustrated through numerical examples.