  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
$\tilde{O}(1/\sqrt{\epsilon})$ gradient evaluations and
$\tilde{O}(1/\epsilon^2)$ 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.
