{
  "id": "2212.01719",
  "version": "v1",
  "published": "2022-12-04T01:39:45.000Z",
  "updated": "2022-12-04T01:39:45.000Z",
  "title": "Deep Galerkin Method for Mean Field Control Problem",
  "authors": [
    "Jingruo Sun",
    "Asaf Cohen"
  ],
  "categories": [
    "math.OC",
    "q-fin.MF"
  ],
  "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-12-04T01:39:45.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "mean field control problem",
      "deep galerkin method",
      "mean-field control problem",
      "value function",
      "unique viscosity solution"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}