# Continuous-time Analysis of Anchor Acceleration

arXiv: https://arxiv.org/abs/2304.00771 · HTML: https://mlsanity.com/paper/2304.00771/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Apr 2023.

## Built on by (most cited first, 4 of 4)

- [Accelerating Value Iteration with Anchoring](https://mlsanity.com/paper/2305.16569/) (2023)
- [Direct Acceleration of Stochastic Root-Finding Without Variance Reduction and Regularization](https://mlsanity.com/paper/2608.12043/) (2026)
- [Understanding Dynamics of Adam in Zero-Sum Games: An ODE Approach](https://mlsanity.com/paper/2605.19392/) (2026)
- [Dual-Anchor Acceleration Is Near-Optimal for Stochastic Monotone Root-Finding](https://mlsanity.com/paper/2609.36033/) (2026)

## Abstract (arXiv)

Recently, the anchor acceleration, an acceleration mechanism distinct from Nesterov's, has been discovered for minimax optimization and fixed-point problems, but its mechanism is not understood well, much less so than Nesterov acceleration. In this work, we analyze continuous-time models of anchor acceleration. We provide tight, unified analyses for characterizing the convergence rate as a function of the anchor coefficient β(t), thereby providing insight into the anchor acceleration mechanism and its accelerated O(1/k2)-convergence rate. Finally, we present an adaptive method inspired by the continuous-time analyses and establish its effectiveness through theoretical analyses and experiments.