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Deep Galerkin Method for Mean Field Control Problem

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  • Jingruo Sun

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.

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  • Jingruo Sun, 2022. "Deep Galerkin Method for Mean Field Control Problem," Papers 2212.01719, arXiv.org, revised Feb 2024.
    • Handle: RePEc:arx:papers:2212.01719
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    References listed on IDEAS

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    1. Justin Sirignano & Konstantinos Spiliopoulos, 2017. "DGM: A deep learning algorithm for solving partial differential equations," Papers 1708.07469, arXiv.org, revised Sep 2018.
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