This paper is devoted to the numerical resolution of McKean-Vlasov control problems via the class of mean-field neural networks introduced in our companion paper [25] in order to learn the solution on the Wasserstein space. We propose several algorithms either based on dynamic programming with control learning by policy or value iteration, or backward SDE from stochastic maximum principle with global or local loss functions. Extensive numerical results on different examples are presented to illustrate the accuracy of each of our eight algorithms. We discuss and compare the pros and cons of all the tested methods.

翻译：本文致力于通过我们在配套论文[25]中引入的均值场神经网络类来数值求解McKean-Vlasov控制问题，以学习Wasserstein空间上的解。我们提出了多种算法，包括基于动态规划的策略迭代或值迭代控制学习方法，以及基于随机最大值原理的全局或局部损失函数的倒向随机微分方程方法。通过不同算例的大量数值结果，展示了我们八种算法各自的精度。我们讨论并比较了所有测试方法的优缺点。