{
  "id": "2102.04397",
  "version": "v1",
  "published": "2021-02-08T18:01:54.000Z",
  "updated": "2021-02-08T18:01:54.000Z",
  "title": "Entropic Optimal Transport: Geometry and Large Deviations",
  "authors": [
    "Espen Bernton",
    "Promit Ghosal",
    "Marcel Nutz"
  ],
  "categories": [
    "math.OC",
    "math.FA",
    "math.PR"
  ],
  "abstract": "We study the convergence of entropically regularized optimal transport to optimal transport. The main result is concerned with the convergence of the associated optimizers and takes the form of a large deviations principle quantifying the local exponential convergence rate as the regularization parameter vanishes. The exact rate function is determined in a general setting and linked to the Kantorovich potential of optimal transport. Our arguments are based on the geometry of the optimizers and inspired by the use of $c$-cyclical monotonicity in classical transport theory. The results can also be phrased in terms of Schr\\\"odinger bridges.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-02-08T18:01:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "90C25",
      "60F10",
      "49N05"
    ],
    "keywords": [
      "entropic optimal transport",
      "local exponential convergence rate",
      "exact rate function",
      "regularization parameter vanishes",
      "main result"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}