# Non-convex Conditional Gradient Sliding

arXiv: https://arxiv.org/abs/1708.04783 · HTML: https://mlsanity.com/paper/1708.04783/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Aug 2017.

## Built on by (most cited first, 12 of 12)

- [Lions and Muons: Optimization via Stochastic Frank-Wolfe under Heavy-Tailed Noise](https://mlsanity.com/paper/2506.04192/) (2025)
- [A Projection-free Algorithm for Constrained Stochastic Multi-level Composition Optimization](https://mlsanity.com/paper/2202.04296/) (2022)
- [Sarah Frank-Wolfe: Methods for Constrained Optimization with Best Rates and Practical Features](https://mlsanity.com/paper/2304.11737/) (2023)
- [Constrained Stochastic Nonconvex Optimization with State-dependent Markov Data](https://mlsanity.com/paper/2206.11346/) (2022)
- [A Variance Controlled Stochastic Method with Biased Estimation for Faster Non-convex Optimization](https://mlsanity.com/paper/2102.09893/) (2021)
- [Projection-Free Functional Constrained Optimization for Risk Aversion and Sparsity Control](https://mlsanity.com/paper/2210.05108/) (2022)
- [Linearization Algorithms for Fully Composite Optimization](https://mlsanity.com/paper/2302.12808/) (2023)
- [Stochastic Constrained Decentralized Optimization for Machine Learning with Fewer Data Oracles: a Gradient Sliding Approach](https://mlsanity.com/paper/2404.02511/) (2024)
- [Projection-Free Variance Reduction Methods for Stochastic Constrained Multi-Level Compositional Optimization](https://mlsanity.com/paper/2406.03787/) (2024)
- [Revisiting Frank-Wolfe for Structured Nonconvex Optimization](https://mlsanity.com/paper/2503.08921/) (2025)
- [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)

We investigate a projection free method, namely conditional gradient sliding on batched, stochastic and finite-sum non-convex problem. CGS is a smart combination of Nesterov's accelerated gradient method and Frank-Wolfe (FW) method, and outperforms FW in the convex setting by saving gradient computations. However, the study of CGS in the non-convex setting is limited. In this paper, we propose the non-convex conditional gradient sliding (NCGS) which surpasses the non-convex Frank-Wolfe method in batched, stochastic and finite-sum setting.