# How Does Momentum Help Frank Wolfe?

arXiv: https://arxiv.org/abs/2006.11116 · HTML: https://mlsanity.com/paper/2006.11116/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Jun 2020.

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

- [Fast Stochastic Composite Minimization and an Accelerated Frank-Wolfe Algorithm under Parallelization](https://mlsanity.com/paper/2205.12751/) (2022)
- [Decision-Focused Evaluation of Worst-Case Distribution Shift](https://mlsanity.com/paper/2407.03557/) (2024)
- [Reducing Discretization Error in the Frank-Wolfe Method](https://mlsanity.com/paper/2304.01432/) (2023)

## Abstract (arXiv)

We unveil the connections between Frank Wolfe (FW) type algorithms and the momentum in Accelerated Gradient Methods (AGM). On the negative side, these connections illustrate why momentum is unlikely to be effective for FW type algorithms. The encouraging message behind this link, on the other hand, is that momentum is useful for FW on a class of problems. In particular, we prove that a momentum variant of FW, that we term accelerated Frank Wolfe (AFW), converges with a faster rate tildecal O(frac1k2) on certain constraint sets despite the same cal O(frac1k) rate as FW on general cases. Given the possible acceleration of AFW at almost no extra cost, it is thus a competitive alternative to FW. Numerical experiments on benchmarked machine learning tasks further validate our theoretical findings.