论文标题
麦基恩 - 维拉索夫控制问题的基于平均场神经网络的算法 *
Mean-field neural networks-based algorithms for McKean-Vlasov control problems *
论文作者
论文摘要
本文致力于通过在我们的伴侣论文[25]中引入的平均场神经网络的麦基 - 维拉索夫控制问题的数值分辨率，以便在Wasserstein空间上学习解决方案。我们提出了几种基于动态编程的算法，并通过策略或价值迭代进行控制学习，或者从随机最大原理中向后SDE，具有全球或本地损失功能。提出了不同示例的广泛数值结果，以说明我们八种算法中每种算法的准确性。我们讨论并比较所有测试方法的利弊。
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.
