  We introduce a new class of Frank-Wolfe algorithms for minimizing
differentiable functionals over probability measures. This framework can be
shown to encompass a diverse range of tasks in areas such as artificial
intelligence, reinforcement learning, and optimization. Concrete computational
complexities for these algorithms are established and demonstrate that these
methods enjoy convergence in regimes that go beyond convexity and require
minimal regularity of the underlying functional. Novel techniques used to
obtain these results also lead to the development of new complexity bounds and
duality theorems for a family of distributionally robust optimization problems.
The performance of our method is demonstrated on several nonparametric
estimation problems.
