# Accelerated Minimax Algorithms Flock Together

arXiv: https://arxiv.org/abs/2205.11093 · HTML: https://mlsanity.com/paper/2205.11093/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 May 2022.

## Built on by (most cited first, 9 of 9)

- [Accelerated Single-Call Methods for Constrained Min-Max Optimization](https://mlsanity.com/paper/2210.03096/) (2022)
- [Towards Weaker Variance Assumptions for Stochastic Optimization](https://mlsanity.com/paper/2504.09951/) (2025)
- [Accelerating Value Iteration with Anchoring](https://mlsanity.com/paper/2305.16569/) (2023)
- [Fundamental Benefit of Alternating Updates in Minimax Optimization](https://mlsanity.com/paper/2402.10475/) (2024)
- [Revisiting Inexact Fixed-Point Iterations for Min-Max Problems: Stochasticity and Structured Nonconvexity](https://mlsanity.com/paper/2402.05071/) (2024)
- [Direct Acceleration of Stochastic Root-Finding Without Variance Reduction and Regularization](https://mlsanity.com/paper/2608.12043/) (2026)
- [On Same-Sample and Independent-Sample Stochastic Extragradient for Monotone Variational Inequalities](https://mlsanity.com/paper/2608.06182/) (2026)
- [Polyak-Type Extragradient Methods for Monotone Root-Finding Problems](https://mlsanity.com/paper/2609.26581/) (2026)
- [Dual-Anchor Acceleration Is Near-Optimal for Stochastic Monotone Root-Finding](https://mlsanity.com/paper/2609.36033/) (2026)

## Abstract (arXiv)

Several new accelerated methods in minimax optimization and fixed-point iterations have recently been discovered, and, interestingly, they rely on a mechanism distinct from Nesterov's momentum-based acceleration. In this work, we show that these accelerated algorithms exhibit what we call the merging path (MP) property; the trajectories of these algorithms merge quickly. Using this novel MP property, we establish point convergence of existing accelerated minimax algorithms and derive new state-of-the-art algorithms for the strongly-convex-strongly-concave setup and for the prox-grad setup.