Integration Methods and Accelerated Optimization Algorithms
Optimization and Control
2017-02-23 v1
Abstract
We show that accelerated optimization methods can be seen as particular instances of multi-step integration schemes from numerical analysis, applied to the gradient flow equation. In comparison with recent advances in this vein, the differential equation considered here is the basic gradient flow and we show that multi-step schemes allow integration of this differential equation using larger step sizes, thus intuitively explaining acceleration results.
Cite
@article{arxiv.1702.06751,
title = {Integration Methods and Accelerated Optimization Algorithms},
author = {Damien Scieur and Vincent Roulet and Francis Bach and Alexandre d'Aspremont},
journal= {arXiv preprint arXiv:1702.06751},
year = {2017}
}