# Lazifying Conditional Gradient Algorithms

arXiv: https://arxiv.org/abs/1610.05120 · HTML: https://mlsanity.com/paper/1610.05120/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Oct 2016.

## Built on by (most cited first, 8 of 8)

- [Complexity of Linear Minimization and Projection on Some Sets](https://mlsanity.com/paper/2101.10040/) (2021)
- [Zeroth and First Order Stochastic Frank-Wolfe Algorithms for Constrained Optimization](https://mlsanity.com/paper/2107.06534/) (2021)
- [Parameter-free Locally Accelerated Conditional Gradients](https://mlsanity.com/paper/2102.06806/) (2021)
- [Interpretable Neural Networks with Frank-Wolfe: Sparse Relevance Maps and Relevance Orderings](https://mlsanity.com/paper/2110.08105/) (2021)
- [Convex mixed-integer optimization with Frank-Wolfe methods](https://mlsanity.com/paper/2208.11010/) (2022)
- [Conditional Gradients for the Approximate Vanishing Ideal](https://mlsanity.com/paper/2202.03349/) (2022)
- [Scalable DC Optimization via Adaptive Frank-Wolfe Algorithms](https://mlsanity.com/paper/2507.17545/) (2025)
- [Scalable Projection-Free Optimization](https://mlsanity.com/paper/2105.03527/) (2021)

## Abstract (arXiv)

Conditional gradient algorithms (also often called Frank-Wolfe algorithms) are popular due to their simplicity of only requiring a linear optimization oracle and more recently they also gained significant traction for online learning. While simple in principle, in many cases the actual implementation of the linear optimization oracle is costly. We show a general method to lazify various conditional gradient algorithms, which in actual computations leads to several orders of magnitude of speedup in wall-clock time. This is achieved by using a faster separation oracle instead of a linear optimization oracle, relying only on few linear optimization oracle calls.