{
  "id": "2410.17297",
  "version": "v1",
  "published": "2024-10-22T07:38:23.000Z",
  "updated": "2024-10-22T07:38:23.000Z",
  "title": "Error estimates between SGD with momentum and underdamped Langevin diffusion",
  "authors": [
    "Arnaud Guillin",
    "Yu Wang",
    "Lihu Xu",
    "Haoran Yang"
  ],
  "categories": [
    "stat.ML",
    "cs.LG",
    "math.PR"
  ],
  "abstract": "Stochastic gradient descent with momentum is a popular variant of stochastic gradient descent, which has recently been reported to have a close relationship with the underdamped Langevin diffusion. In this paper, we establish a quantitative error estimate between them in the 1-Wasserstein and total variation distances.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-10-22T07:38:23.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "underdamped langevin diffusion",
      "stochastic gradient descent",
      "total variation distances",
      "close relationship",
      "popular variant"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}