{
  "id": "1709.06466",
  "version": "v1",
  "published": "2017-09-19T14:47:58.000Z",
  "updated": "2017-09-19T14:47:58.000Z",
  "title": "Evaluation of the Rate of Convergence in the PIA",
  "authors": [
    "Jun Maeda",
    "Saul D. Jacka"
  ],
  "comment": "11 pages, 3 figures",
  "categories": [
    "math.OC",
    "math.NA"
  ],
  "abstract": "Folklore says that Howard's Policy Improvement Algorithm converges extraordinarily fast, even for controlled diffusion settings. In a previous paper, we proved that approximations of the solution of a particular parabolic partial differential equation obtained via the policy improvement algorithm show a quadratic local convergence. In this paper, we show that we obtain the same rate of convergence of the algorithm in a more general setup. This provides some explanation as to why the algorithm converges fast. We provide an example by solving a semilinear elliptic partial differential equation numerically by applying the algorithm and check how the approximations converge to the analytic solution.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-09-19T14:47:58.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "convergence",
      "semilinear elliptic partial differential equation",
      "improvement algorithm converges extraordinarily fast",
      "howards policy improvement algorithm converges"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}