ICML 2018oral32 citations

Non-convex Conditional Gradient Sliding

Chao Qu, Yan Li, Huan Xu

Abstract

We investigate a projection free optimization method, namely non-convex conditional gradient sliding (NCGS) for non-convex optimization problems on the batch, stochastic and finite-sum settings. Conditional gradient sliding (CGS) method, by integrating Nesterov’s accelerated gradient method with Frank-Wolfe (FW) method in a smart way, outperforms FW for convex optimization, by reducing the amount of 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) methods and analyze their convergence properties. We also leverage the idea of variance reduction from the recent progress in convex optimization to obtain a new algorithm termed

BibTeX
@InProceedings{pmlr-v80-qu18a,
  title = 	 {Non-convex Conditional Gradient Sliding},
  author =       {Qu, Chao and Li, Yan and Xu, Huan},
  booktitle = 	 {Proceedings of the 35th International Conference on Machine Learning},
  pages = 	 {4208--4217},
  year = 	 {2018},
  editor = 	 {Dy, Jennifer and Krause, Andreas},
  volume = 	 {80},
  series = 	 {Proceedings of Machine Learning Research},
  month = 	 {10--15 Jul},
  publisher =    {PMLR},
  pdf = 	 {http://proceedings.mlr.press/v80/qu18a/qu18a.pdf},
  url = 	 {https://proceedings.mlr.press/v80/qu18a.html},
  abstract = 	 {We investigate a projection free optimization method, namely non-convex conditional gradient sliding (NCGS) for non-convex optimization problems on the batch, stochastic and finite-sum settings. Conditional gradient sliding (CGS) method, by integrating Nesterov’s accelerated gradient method with Frank-Wolfe (FW) method in a smart way, outperforms FW for convex optimization, by reducing the amount of 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) methods and analyze their convergence properties. We also leverage the idea of variance reduction from the recent progress in convex optimization to obtain a new algorithm termed