{
  "id": "1711.10754",
  "version": "v1",
  "published": "2017-11-29T10:13:01.000Z",
  "updated": "2017-11-29T10:13:01.000Z",
  "title": "Stochastic Approximation on Riemannian manifolds",
  "authors": [
    "Suhail M. Shah"
  ],
  "comment": "28 pages, 1 Figure",
  "categories": [
    "math.OC"
  ],
  "abstract": "The standard theory of stochastic approximation (SA) is extended to the case when the constraint set is a Riemannian manifold. Specifically, the standard ODE method for analyzing SA schemes is extended to iterations constrained to stay on a manifold using a retraction mapping. In addition, for submanifolds of a Euclidean space, a framework is developed for a projected SA scheme with approximate retractions. The framework is also extended to non-differentiable constraint sets.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-11-29T10:13:01.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "riemannian manifold",
      "stochastic approximation",
      "standard ode method",
      "standard theory",
      "approximate retractions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}