{
  "id": "2312.00640",
  "version": "v1",
  "published": "2023-12-01T15:00:59.000Z",
  "updated": "2023-12-01T15:00:59.000Z",
  "title": "One to beat them all: \"RYU'' -- a unifying framework for the construction of safe balls",
  "authors": [
    "Thu-Le Tran",
    "Clément Elvira",
    "Hong-Phuong Dang",
    "Cédric Herzet"
  ],
  "comment": "19 pages, 1 table",
  "categories": [
    "math.OC",
    "cs.LG",
    "stat.ML"
  ],
  "abstract": "In this paper, we put forth a novel framework (named ``RYU'') for the construction of ``safe'' balls, i.e. regions that provably contain the dual solution of a target optimization problem. We concentrate on the standard setup where the cost function is the sum of two terms: a closed, proper, convex Lipschitz-smooth function and a closed, proper, convex function. The RYU framework is shown to generalize or improve upon all the results proposed in the last decade for the considered family of optimization problems.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-12-01T15:00:59.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "safe balls",
      "unifying framework",
      "construction",
      "target optimization problem",
      "convex lipschitz-smooth function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}