Deep Galerkin Method for Mean Field Control Problem
Abstract
We consider an optimal control problem where the average welfare of weakly interacting agents is of interest. We examine the mean-field control problem as the fluid approximation of the N-agent control problem with the setup of finite-state space, continuous-time, and finite-horizon. The value function of the mean-field control problem is characterized as the unique viscosity solution of a Hamilton-Jacobi-Bellman equation in the simplex. We apply the DGM to estimate the value function and the evolution of the distribution. We also prove the numerical solution approximated by a neural network converges to the analytical solution.
Cite
@article{arxiv.2212.01719,
title = {Deep Galerkin Method for Mean Field Control Problem},
author = {Jingruo Sun},
journal= {arXiv preprint arXiv:2212.01719},
year = {2024}
}
Comments
This submission has been withdrawn by arXiv administrators as the second author was added without their knowledge or consent