# Improved Convergence Factor of Windowed Anderson Acceleration for Symmetric Fixed-Point Iterations

arXiv: https://arxiv.org/abs/2311.02490 · HTML: https://mlsanity.com/paper/2311.02490/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 38 references that are in the map.
- First posted on arXiv 4 Nov 2023.

## Builds on (most cited first, 11 of 11)

- [Acceleration Methods](https://mlsanity.com/paper/2101.09545/) (2021)
- [Globally Convergent Type-I Anderson Acceleration for Non-Smooth Fixed-Point Iterations](https://mlsanity.com/paper/1808.03971/) (2018)
- [Regularized Nonlinear Acceleration](https://mlsanity.com/paper/1606.04133/) (2016)
- [Anderson Acceleration for Reinforcement Learning](https://mlsanity.com/paper/1809.09501/) (2018)
- [Rigorous Guarantees for Tyler's M-estimator via quantum expansion](https://mlsanity.com/paper/2002.00071/) (2020)
- [Regularized Anderson Acceleration for Off-Policy Deep Reinforcement Learning](https://mlsanity.com/paper/1909.03245/) (2019)
- [Damped Anderson Mixing for Deep Reinforcement Learning: Acceleration, Convergence, and Stabilization](https://mlsanity.com/paper/2110.08896/) (2021)
- [Anderson acceleration of coordinate descent](https://mlsanity.com/paper/2011.10065/) (2020)
- [Anderson Acceleration for Nonsmooth Fixed Point Problems](https://mlsanity.com/paper/2209.10336/) (2022)
- [Generalized Framework for Nonlinear Acceleration](https://mlsanity.com/paper/1903.08764/) (2019)
- [Linear Asymptotic Convergence of Anderson Acceleration: Fixed-Point Analysis](https://mlsanity.com/paper/2109.14176/) (2021)

## Abstract (arXiv)

This paper studies the commonly utilized windowed Anderson acceleration (AA) algorithm for fixed-point methods, x(k+1)=q(x(k)). It provides the first proof that when the operator q is linear and symmetric the windowed AA, which uses a sliding window of prior iterates, improves the root-linear convergence factor over the fixed-point iterations. When q is nonlinear, yet has a symmetric Jacobian at a fixed point, a slightly modified AA algorithm is proved to have an analogous root-linear convergence factor improvement over fixed-point iterations. Simulations verify our observations. Furthermore, experiments with different data models demonstrate AA is significantly superior to the standard fixed-point methods for Tyler's M-estimation.