{
  "id": "2209.01256",
  "version": "v1",
  "published": "2022-09-02T20:04:30.000Z",
  "updated": "2022-09-02T20:04:30.000Z",
  "title": "A PDE approach for regret bounds under partial monitoring",
  "authors": [
    "Erhan Bayraktar",
    "Ibrahim Ekren",
    "Xin Zhang"
  ],
  "comment": "Keywords: machine learning, expert advice framework, bandit problem, asymptotic expansion, Wasserstein derivative",
  "categories": [
    "math.PR",
    "cs.LG",
    "math.OC"
  ],
  "abstract": "In this paper, we study a learning problem in which a forecaster only observes partial information. By properly rescaling the problem, we heuristically derive a limiting PDE on Wasserstein space which characterizes the asymptotic behavior of the regret of the forecaster. Using a verification type argument, we show that the problem of obtaining regret bounds and efficient algorithms can be tackled by finding appropriate smooth sub/supersolutions of this parabolic PDE.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-09-02T20:04:30.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "pde approach",
      "partial monitoring",
      "finding appropriate smooth sub/supersolutions",
      "verification type argument",
      "forecaster"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}