# Backtracking linesearch for conditional gradient sliding

arXiv: https://arxiv.org/abs/2006.05272 · HTML: https://mlsanity.com/paper/2006.05272/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Jun 2020.

## Built on by (most cited first, 1 of 1)

- [Stochastic Constrained Decentralized Optimization for Machine Learning with Fewer Data Oracles: a Gradient Sliding Approach](https://mlsanity.com/paper/2404.02511/) (2024)

## Abstract (arXiv)

We present a modification of the conditional gradient sliding (CGS) method that was originally developed in citelan2016conditional. While the CGS method is a theoretical breakthrough in the theory of projection-free first-order methods since it is the first that reaches the theoretical performance limit, in implementation it requires the knowledge of the Lipschitz constant of the gradient of the objective function L and the number of total gradient evaluations N. Such requirements imposes difficulties in the actual implementation, not only because that it can be difficult to choose proper values of L and N that satisfies the conditions for convergence, but also since conservative choices of L and N can deteriorate the practical numerical performance of the CGS method. Our proposed method, called the conditional gradient sliding method with linesearch (CGS-ls), does not require the knowledge of either L and N, and is able to terminate early before the theoretically required number of iterations. While more practical in numerical implementation, the theoretical performance of our proposed CGS-ls method is still as good as that of the CGS method. We present numerical experiments to show the efficiency of our proposed method in practice.