{
  "id": "math/0405287",
  "version": "v1",
  "published": "2004-05-14T15:13:12.000Z",
  "updated": "2004-05-14T15:13:12.000Z",
  "title": "Convergence rate of linear two-time-scale stochastic approximation",
  "authors": [
    "Vijay R. Konda",
    "John N. Tsitsiklis"
  ],
  "journal": "Annals of Applied Probability 2004, Vol. 14, No. 2, 796-819",
  "doi": "10.1214/105051604000000116",
  "categories": [
    "math.PR"
  ],
  "abstract": "We study the rate of convergence of linear two-time-scale stochastic approximation methods. We consider two-time-scale linear iterations driven by i.i.d. noise, prove some results on their asymptotic covariance and establish asymptotic normality. The well-known result [Polyak, B. T. (1990). Automat. Remote Contr. 51 937-946; Ruppert, D. (1988). Technical Report 781, Cornell Univ.] on the optimality of Polyak-Ruppert averaging techniques specialized to linear stochastic approximation is established as a consequence of the general results in this paper.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-05-14T15:13:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "62L20"
    ],
    "keywords": [
      "convergence rate",
      "linear two-time-scale stochastic approximation methods",
      "two-time-scale linear iterations driven",
      "linear stochastic approximation",
      "asymptotic covariance"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......5287K"
    }
  }
}