论文标题
鞍点问题有效的无投影算法
Efficient Projection-Free Algorithms for Saddle Point Problems
论文作者
论文摘要
Frank-Wolfe算法是限制优化问题的经典方法。最近，它在许多机器学习应用程序中很受欢迎，因为它的无投影属性会导致更有效的迭代。在本文中，我们研究了具有复杂约束的凸侧符号鞍点问题的无投影算法。我们的方法将条件梯度滑动与镜像结合在一起，并表明它仅需要$ \ tilde {o}（1/\sqrtε）$梯度评估和$ \ tilde {o}（1/ε^2）$ linearize $ linalear优化在批处理设置中。我们还将我们的方法扩展到随机设置，并提出第一个随机投影算法，以解决鞍点问题。实验结果证明了我们的算法的有效性并验证了我们的理论保证。
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.
