{
  "id": "1705.07260",
  "version": "v1",
  "published": "2017-05-20T04:33:10.000Z",
  "updated": "2017-05-20T04:33:10.000Z",
  "title": "Oracle Complexity of Second-Order Methods for Smooth Convex Optimization",
  "authors": [
    "Ohad Shamir",
    "Ron Shiff"
  ],
  "comment": "28 pages",
  "categories": [
    "math.OC"
  ],
  "abstract": "Second-order methods, which utilize gradients as well as Hessians to optimize a given function, are of major importance in mathematical optimization. In this work, we study the oracle complexity of such methods, or equivalently, the number of iterations required to optimize a function to a given accuracy. Focusing on smooth and convex functions, we derive (to the best of our knowledge) the first algorithm-independent lower bounds for such methods. These bounds shed light on the limits of attainable performance with second-order methods, and in which cases they can or cannot require less iterations than gradient-based methods, whose oracle complexity is much better understood.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-05-20T04:33:10.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "second-order methods",
      "oracle complexity",
      "smooth convex optimization",
      "first algorithm-independent lower bounds",
      "iterations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}