# Nonlinear Acceleration of Stochastic Algorithms

arXiv: https://arxiv.org/abs/1706.07270 · HTML: https://mlsanity.com/paper/1706.07270/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Jun 2017.

## Built on by (most cited first, 3 of 3)

- [On Efficient Training of Large-Scale Deep Learning Models: A Literature Review](https://mlsanity.com/paper/2304.03589/) (2023)
- [Stochastic Anderson Mixing for Nonconvex Stochastic Optimization](https://mlsanity.com/paper/2110.01543/) (2021)
- [Anderson acceleration for iteratively reweighted ℓ1 algorithm](https://mlsanity.com/paper/2403.07271/) (2024)

## Abstract (arXiv)

Extrapolation methods use the last few iterates of an optimization algorithm to produce a better estimate of the optimum. They were shown to achieve optimal convergence rates in a deterministic setting using simple gradient iterates. Here, we study extrapolation methods in a stochastic setting, where the iterates are produced by either a simple or an accelerated stochastic gradient algorithm. We first derive convergence bounds for arbitrary, potentially biased perturbations, then produce asymptotic bounds using the ratio between the variance of the noise and the accuracy of the current point. Finally, we apply this acceleration technique to stochastic algorithms such as SGD, SAGA, SVRG and Katyusha in different settings, and show significant performance gains.