Year: 2020
Type: preprint
Abstract: 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 shows that it only requires $\tilde{O}(1/\sqrtε)$ gradient evaluations and $\tilde{O}(1/ε^2)$ 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.
Source: arXiv (Cornell University)
Authors: Chen, Cheng, Luo, Luo, Zhang, Weinan, Yu, Yong
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3093821799