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.

翻译：我们引入了一种新的弗兰克-沃夫算法,以尽可能减少与概率计量相比的不同功能。这个框架可以证明包含人工智能、强化学习和优化等领域的各种任务。这些算法的具体计算复杂性已经确立,并表明这些方法在超出复杂程度和要求基本功能最低常规性的制度中具有趋同性。用于取得这些结果的新技术还导致开发新的复杂界限和双元理论,用于分配性强优化问题大家庭。我们方法的性能在若干非参数估算问题中得到了证明。