Mean-field neural networks-based algorithms for McKean-Vlasov control problems *

TL;DR

This paper develops and compares eight neural network-based algorithms for numerically solving McKean-Vlasov control problems, demonstrating their effectiveness through extensive numerical experiments.

Contribution

It introduces multiple novel neural network algorithms for McKean-Vlasov control problems, including dynamic programming and backward SDE approaches, with comprehensive performance analysis.

Findings

Algorithms achieve high accuracy on various examples

Dynamic programming methods outperform some alternatives in certain cases

Neural network approaches are effective for high-dimensional Wasserstein space problems

Abstract

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.