  The conditional gradient idea proposed by Marguerite Frank and Philip Wolfe
in 1956 was so well received by the community that new algorithms (also called
Frank--Wolfe type algorithms) are still being actively created. In this paper,
we study a non-smooth stochastic convex optimization problem with constraints.
Using a smoothing technique and based on an accelerated batched first-order
Stochastic Conditional Gradient Sliding method, we propose a novel
gradient-free Frank--Wolfe type algorithm called Zero-Order Stochastic
Conditional Gradient Sliding (ZO-SCGS). This algorithm is robust not only for
the class of non-smooth problems, but surprisingly also for the class of smooth
black box problems, outperforming the SOTA algorithms in the smooth case in
term oracle calls. In practical experiments we confirm our theoretical results.
