{
  "id": "1602.05394",
  "version": "v1",
  "published": "2016-02-17T12:57:08.000Z",
  "updated": "2016-02-17T12:57:08.000Z",
  "title": "Online optimization and regret guarantees for non-additive long-term constraints",
  "authors": [
    "Rodolphe Jenatton",
    "Jim Huang",
    "Cedric Archambeau"
  ],
  "categories": [
    "stat.ML",
    "cs.LG",
    "math.OC",
    "math.ST",
    "stat.TH"
  ],
  "abstract": "We consider online optimization in the 1-lookahead setting, where the objective does not decompose additively over the rounds of the online game. The resulting formulation enables us to deal with non-stationary and/or long-term constraints , which arise, for example, in online display advertising problems. We propose an on-line primal-dual algorithm for which we obtain dynamic cumulative regret guarantees. They depend on the convexity and the smoothness of the non-additive penalty, as well as terms capturing the smoothness with which the residuals of the non-stationary and long-term constraints vary over the rounds. We conduct experiments on synthetic data to illustrate the benefits of the non-additive penalty and show vanishing regret convergence on live traffic data collected by a display advertising platform in production.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-02-17T12:57:08.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "non-additive long-term constraints",
      "online optimization",
      "online display advertising problems",
      "on-line primal-dual algorithm",
      "dynamic cumulative regret guarantees"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}