Efficient Projection-free Algorithms for Saddle Point Problems

Part of Advances in Neural Information Processing Systems 33 (NeurIPS 2020)

AuthorFeedback Bibtex MetaReview Paper Review Supplemental


Cheng Chen, Luo Luo, Weinan Zhang, Yong Yu


The Frank-Wolfe algorithm is a classic method for constrained optimization problems. It has recently been popular in many machine learning applications because its projection-free property leads to more efficient iterations. In this paper, we study projection-free algorithms for convex-strongly-concave saddle point problems with complicated constraints. Our method combines Conditional Gradient Sliding with Mirror-Prox and show that it only requires $\tilde{\cO}(1/\sqrt{\epsilon})$ gradient evaluations and $\tilde{\cO}(1/\epsilon^2)$ linear optimizations in the batch setting. We also extend our method to the stochastic setting and propose first stochastic projection-free algorithms for saddle point problems. Experimental results demonstrate the effectiveness of our algorithms and verify our theoretical guarantees.