# An Improved Last-Iterate Convergence Rate for Anchored Gradient Descent Ascent

arXiv: https://arxiv.org/abs/2604.03782 · HTML: https://mlsanity.com/paper/2604.03782/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 20 references that are in the map.
- First posted on arXiv 4 Apr 2026.

## Builds on (most cited first, 16 of 16)

- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [A Reductions Approach to Fair Classification](https://mlsanity.com/paper/1803.02453/) (2018)
- [Training GANs with Optimism](https://mlsanity.com/paper/1711.00141/) (2017)
- [On the convergence of single-call stochastic extra-gradient methods](https://mlsanity.com/paper/1908.08465/) (2019)
- [Fast Extra Gradient Methods for Smooth Structured Nonconvex-Nonconcave Minimax Problems](https://mlsanity.com/paper/2106.02326/) (2021)
- [Halpern Iteration for Near-Optimal and Parameter-Free Monotone Inclusion and Strong Solutions to Variational Inequalities](https://mlsanity.com/paper/2002.08872/) (2020)
- [Stochastic Variance Reduction Methods for Policy Evaluation](https://mlsanity.com/paper/1702.07944/) (2017)
- [Tight last-iterate convergence rates for no-regret learning in multi-player games](https://mlsanity.com/paper/2010.13724/) (2020)
- [Last-Iterate Convergence of Optimistic Gradient Method for Monotone Variational Inequalities](https://mlsanity.com/paper/2205.08446/) (2022)
- [Accelerated Single-Call Methods for Constrained Min-Max Optimization](https://mlsanity.com/paper/2210.03096/) (2022)
- [Structured Optimal Transport](https://mlsanity.com/paper/1712.06199/) (2017)
- [Near-Optimal Algorithms for Making the Gradient Small in Stochastic Minimax Optimization](https://mlsanity.com/paper/2208.05925/) (2022)
- [Tight Last-Iterate Convergence of the Extragradient and the Optimistic Gradient Descent-Ascent Algorithm for Constrained Monotone Variational Inequalities](https://mlsanity.com/paper/2204.09228/) (2022)
- [ODE Analysis of Stochastic Gradient Methods with Optimism and Anchoring for Minimax Problems](https://mlsanity.com/paper/1905.10899/) (2019)
- [Negative Stepsizes Make Gradient-Descent-Ascent Converge](https://mlsanity.com/paper/2505.01423/) (2025)
- [Semi-Anchored Multi-Step Gradient Descent Ascent Method for Structured Nonconvex-Nonconcave Composite Minimax Problems](https://mlsanity.com/paper/2105.15042/) (2021)

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

- [Advancing Mathematics Research with AI-Driven Formal Proof Search](https://mlsanity.com/paper/2605.22763/) (2026)
- [A Unifying View of Anchoring via Operator-Side Tikhonov Regularization](https://mlsanity.com/paper/2605.30905/) (2026)
- [Accelerated and Stable Convergence with Anchored Generalized Optimistic Method](https://mlsanity.com/paper/2606.21528/) (2026)

## Abstract (arXiv)

We analyze the last-iterate convergence of the Anchored Gradient Descent Ascent algorithm for smooth convex-concave min-max problems. While previous work established a last-iterate rate of O(1/t2-2p) for the squared gradient norm, where p ∈ (1/2, 1), it remained an open problem whether the improved exact O(1/t) rate is achievable. In this work, we resolve this question in the affirmative. This result was discovered autonomously by an AI system capable of writing formal proofs in Lean. The Lean proof can be accessed at https://github.com/google-deepmind/formal-conjectures/pull/3675/commits/a13226b49fd3b897f4c409194f3bcbeb96a08515