# Frank-Wolfe with Subsampling Oracle

arXiv: https://arxiv.org/abs/1803.07348 · HTML: https://mlsanity.com/paper/1803.07348/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Mar 2018.

## Built on by (most cited first, 6 of 6)

- [Zeroth and First Order Stochastic Frank-Wolfe Algorithms for Constrained Optimization](https://mlsanity.com/paper/2107.06534/) (2021)
- [Fast online ranking with fairness of exposure](https://mlsanity.com/paper/2209.13019/) (2022)
- [Contextual bandits with concave rewards, and an application to fair ranking](https://mlsanity.com/paper/2210.09957/) (2022)
- [Generating Structured Adversarial Attacks Using Frank-Wolfe Method](https://mlsanity.com/paper/2102.07360/) (2021)
- [Approximate Frank-Wolfe Algorithms over Graph-structured Support Sets](https://mlsanity.com/paper/2107.00472/) (2021)
- [Zeroth-Order Stackelberg Control in Combinatorial Congestion Games](https://mlsanity.com/paper/2602.23277/) (2026)

## Abstract (arXiv)

We analyze two novel randomized variants of the Frank-Wolfe (FW) or conditional gradient algorithm. While classical FW algorithms require solving a linear minimization problem over the domain at each iteration, the proposed method only requires to solve a linear minimization problem over a small subset of the original domain. The first algorithm that we propose is a randomized variant of the original FW algorithm and achieves a O(1/t) sublinear convergence rate as in the deterministic counterpart. The second algorithm is a randomized variant of the Away-step FW algorithm, and again as its deterministic counterpart, reaches linear (i.e., exponential) convergence rate making it the first provably convergent randomized variant of Away-step FW. In both cases, while subsampling reduces the convergence rate by a constant factor, the linear minimization step can be a fraction of the cost of that of the deterministic versions, especially when the data is streamed. We illustrate computational gains of the algorithms on regression problems, involving both ℓ1 and latent group lasso penalties.