{
  "id": "1705.01091",
  "version": "v1",
  "published": "2017-05-02T17:56:54.000Z",
  "updated": "2017-05-02T17:56:54.000Z",
  "title": "PDE approach to the problem of online prediction with expert advice: a construction of potential-based strategies",
  "authors": [
    "Dmitry B. Rokhlin"
  ],
  "comment": "7 pages",
  "categories": [
    "cs.LG"
  ],
  "abstract": "We consider a sequence of repeated prediction games and formally pass to the limit. The supersolutions of the resulting non-linear parabolic partial differential equation are closely related to the potential functions in the sense of N.\\,Cesa-Bianci, G.\\,Lugosi (2003). Any such supersolution gives an upper bound for forecaster's regret and suggests a potential-based prediction strategy, satisfying the Blackwell condition. A conventional upper bound for the worst-case regret is justified by a simple verification argument.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-05-02T17:56:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "68T05",
      "68W27",
      "35K55"
    ],
    "keywords": [
      "expert advice",
      "online prediction",
      "pde approach",
      "potential-based strategies",
      "non-linear parabolic partial differential equation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}