{
  "id": "1905.07436",
  "version": "v1",
  "published": "2019-05-17T18:45:26.000Z",
  "updated": "2019-05-17T18:45:26.000Z",
  "title": "A Dynamical Systems Perspective on Nesterov Acceleration",
  "authors": [
    "Michael Muehlebach",
    "Michael I. Jordan"
  ],
  "comment": "11 pages, 4 figures, to appear in the Proceedings of the 36th International Conference on Machine Learning",
  "categories": [
    "math.OC",
    "cs.LG",
    "cs.SY",
    "stat.ML"
  ],
  "abstract": "We present a dynamical system framework for understanding Nesterov's accelerated gradient method. In contrast to earlier work, our derivation does not rely on a vanishing step size argument. We show that Nesterov acceleration arises from discretizing an ordinary differential equation with a semi-implicit Euler integration scheme. We analyze both the underlying differential equation as well as the discretization to obtain insights into the phenomenon of acceleration. The analysis suggests that a curvature-dependent damping term lies at the heart of the phenomenon. We further establish connections between the discretized and the continuous-time dynamics.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-05-17T18:45:26.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "dynamical systems perspective",
      "semi-implicit euler integration scheme",
      "nesterov acceleration arises",
      "ordinary differential equation",
      "understanding nesterovs accelerated gradient method"
    ],
    "tags": [
      "conference paper"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}