Numerical resolution of McKean-Vlasov FBSDEs using neural networks

TL;DR

This paper introduces neural network-based algorithms to numerically solve McKean-Vlasov FBSDEs, effectively addressing mean field games and control problems in moderate dimensions.

Contribution

It presents novel neural network schemes for solving McKean-Vlasov FBSDEs, capable of handling complex mean field problems.

Findings

Algorithms successfully solve non-linear quadratic models

Methods perform well in moderate dimensions

Neural networks effectively approximate solutions and gradients

Abstract

We propose several algorithms to solve McKean-Vlasov Forward Backward Stochastic Differential Equations. Our schemes rely on the approximating power of neural networks to estimate the solution or its gradient through minimization problems. As a consequence, we obtain methods able to tackle both mean field games and mean field control problems in moderate dimension. We analyze the numerical behavior of our algorithms on several examples including non linear quadratic models.