# Optimal Acceleration for Minimax and Fixed-Point Problems is Not Unique

arXiv: https://arxiv.org/abs/2404.13228 · HTML: https://mlsanity.com/paper/2404.13228/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Apr 2024.

## Built on by (most cited first, 7 of 7)

- [Negative Stepsizes Make Gradient-Descent-Ascent Converge](https://mlsanity.com/paper/2505.01423/) (2025)
- [Multiplayer Federated Learning: Reaching Equilibrium with Less Communication](https://mlsanity.com/paper/2501.08263/) (2025)
- [Direct Acceleration of Stochastic Root-Finding Without Variance Reduction and Regularization](https://mlsanity.com/paper/2608.12043/) (2026)
- [Accelerated and Stable Convergence with Anchored Generalized Optimistic Method](https://mlsanity.com/paper/2606.21528/) (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)

Recently, accelerated algorithms using the anchoring mechanism for minimax optimization and fixed-point problems have been proposed, and matching complexity lower bounds establish their optimality. In this work, we present the surprising observation that the optimal acceleration mechanism in minimax optimization and fixed-point problems is not unique. Our new algorithms achieve exactly the same worst-case convergence rates as existing anchor-based methods while using materially different acceleration mechanisms. Specifically, these new algorithms are dual to the prior anchor-based accelerated methods in the sense of H-duality. This finding opens a new avenue of research on accelerated algorithms since we now have a family of methods that empirically exhibit varied characteristics while having the same optimal worst-case guarantee.