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Anderson acceleration is a well-established and simple technique for speeding up fixed-point computations with countless applications. Previous studies of Anderson acceleration in optimization have only been able to provide convergence…

Optimization and Control · Mathematics 2020-06-16 Vien V. Mai , Mikael Johansson

Anderson acceleration (AA) is a well-known method for accelerating the convergence of iterative algorithms, with applications in various fields including deep learning and optimization. Despite its popularity in these areas, the…

Machine Learning · Computer Science 2023-08-25 Sarwan Ali , Prakash Chourasia , Murray Patterson

Two adaptive relaxation strategies are proposed for Anderson acceleration. They are specifically designed for applications in which mappings converge to a fixed point. Their superiority over alternative Anderson acceleration is demonstrated…

Numerical Analysis · Mathematics 2024-09-02 Nicolas Lepage-Saucier

Anderson acceleration (AA) as an efficient technique for speeding up the convergence of fixed-point iterations may be designed for accelerating an optimization method. We propose a novel optimization algorithm by adapting Anderson…

Optimization and Control · Mathematics 2022-11-17 Hailiang Liu , Jia-Hao He , Xuping Tian

Anderson acceleration (AA) is an extrapolation technique designed to speed-up fixed-point iterations like those arising from the iterative training of DL models. Training DL models requires large datasets processed in randomly sampled…

Machine Learning · Computer Science 2021-10-29 Massimiliano Lupo Pasini , Junqi Yin , Viktor Reshniak , Miroslav Stoyanov

Anderson acceleration is an effective technique for enhancing the efficiency of fixed-point iterations; however, analyzing its convergence in nonsmooth settings presents significant challenges. In this paper, we investigate a class of…

Optimization and Control · Mathematics 2024-10-16 Kexin Li , Luwei Bai , Xiao Wang , Hao Wang

Anderson Acceleration is a well-established method that allows to speed up or encourage convergence of fixed-point iterations. It has been successfully used in a variety of applications, in particular within the Self-Consistent Field (SCF)…

Numerical Analysis · Mathematics 2024-10-08 Ning Wan , Agnieszka Międlar

Anderson mixing has been heuristically applied to reinforcement learning (RL) algorithms for accelerating convergence and improving the sampling efficiency of deep RL. Despite its heuristic improvement of convergence, a rigorous…

Machine Learning · Computer Science 2021-10-22 Ke Sun , Yafei Wang , Yi Liu , Yingnan Zhao , Bo Pan , Shangling Jui , Bei Jiang , Linglong Kong

Although Anderson acceleration (AA) is known to speed up fixed-point iterations, it is rarely applied in constrained optimization, in particular sequential quadratic programming (SQP). We show that the local convergence behavior of a…

Optimization and Control · Mathematics 2026-04-17 Jonathan Frey , David Kiessling , Katrin Baumgärtner , Moritz Diehl

Many computer graphics problems require computing geometric shapes subject to certain constraints. This often results in non-linear and non-convex optimization problems with globally coupled variables, which pose great challenge for…

Graphics · Computer Science 2018-05-16 Yue Peng , Bailin Deng , Juyong Zhang , Fanyu Geng , Wenjie Qin , Ligang Liu

This paper provides the first proof that Anderson acceleration (AA) improves the convergence rate of general fixed point iterations. AA has been used for decades to speed up nonlinear solvers in many applications, however a rigorous…

Numerical Analysis · Mathematics 2019-02-22 Claire Evans , Sara Pollock , Leo G. Rebholz , Mengying Xiao

Anderson acceleration (AA) is a technique for accelerating the convergence of fixed-point iterations. In this paper, we apply AA to a sequence of functions and modify the norm in its internal optimization problem to the $\mathcal{H}^{-s}$…

Numerical Analysis · Mathematics 2021-09-14 Yunan Yang , Alex Townsend , Daniel Appelö

We present a novel approach for accelerating AI performance by leveraging Anderson extrapolation, a vector-to-vector mapping technique based on a window of historical iterations. By identifying the crossover point (Fig. 1) where a mixing…

Machine Learning · Computer Science 2024-12-20 Saleem Abdul Fattah Ahmed Al Dajani , David E. Keyes

Anderson Acceleration (AA) is a popular acceleration technique to enhance the convergence of fixed-point iterations. The analysis of AA approaches typically focuses on the convergence behavior of a corresponding fixed-point residual, while…

Optimization and Control · Mathematics 2023-09-26 Wenqing Ouyang , Yang Liu , Andre Milzarek

Model-free deep reinforcement learning (RL) algorithms have been widely used for a range of complex control tasks. However, slow convergence and sample inefficiency remain challenging problems in RL, especially when handling continuous and…

Machine Learning · Computer Science 2021-12-07 Wenjie Shi , Shiji Song , Hui Wu , Ya-Chu Hsu , Cheng Wu , Gao Huang

This work proposes a general strategy for solving possibly nonlinear problems arising from implicit time discretizations as a sequence of explicit solutions. The resulting sequence may exhibit instabilities similar to those of the base…

Numerical Analysis · Mathematics 2025-10-21 Nicolas A. Barnafi , Felipe Galarce , Pablo Brubeck

The alternating direction method of multipliers (ADMM) is a popular approach for solving optimization problems that are potentially non-smooth and with hard constraints. It has been applied to various computer graphics applications,…

Graphics · Computer Science 2019-09-04 Juyong Zhang , Yue Peng , Wenqing Ouyang , Bailin Deng

Anderson acceleration (or Anderson mixing) is an efficient acceleration method for fixed point iterations $x_{t+1}=G(x_t)$, e.g., gradient descent can be viewed as iteratively applying the operation $G(x) \triangleq x-\alpha\nabla f(x)$. It…

Optimization and Control · Mathematics 2020-03-03 Zhize Li , Jian Li

Anderson acceleration (AA) is widely used for accelerating the convergence of nonlinear fixed-point methods $x_{k+1}=q(x_{k})$, $x_k \in \mathbb{R}^n$, but little is known about how to quantify the convergence acceleration provided by AA.…

Numerical Analysis · Mathematics 2023-02-27 Hans De Sterck , Yunhui He , Oliver A. Krzysik

In this paper we consider the neural network optimization. We develop Anderson-type acceleration method for the stochastic gradient decent method and it improves the network permanence very much. We demonstrate the applicability of the…

Numerical Analysis · Mathematics 2025-12-11 Kazufumi Ito , Tiancheng Xue
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