Essec\Faculty\Model\Contribution {#2190
  #_index: "academ_contributions"
  #_id: "13868"
  #_source: array:26 [
    "id" => "13868"
    "slug" => "deviation-inequalities-for-stochastic-approximation-by-averaging"
    "yearMonth" => "2022-10"
    "year" => "2022"
    "title" => "Deviation inequalities for stochastic approximation by averaging"
    "description" => "FAN, X., ALQUIER, P. et DOUKHAN, P. (2022). Deviation inequalities for stochastic approximation by averaging. <i>Stochastic Processes and their Applications</i>, 152, pp. 452-485."
    "authors" => array:3 [
      0 => array:3 [
        "name" => "ALQUIER Pierre"
        "bid" => "B00809923"
        "slug" => "alquier-pierre"
      ]
      1 => array:1 [
        "name" => "FAN Xiequan"
      ]
      2 => array:1 [
        "name" => "DOUKHAN Paul"
      ]
    ]
    "ouvrage" => ""
    "keywords" => array:5 [
      0 => "Deviation inequalities"
      1 => "Martingales"
      2 => "Iterated random functions"
      3 => "Stochastic approximation by averaging"
      4 => "Empirical risk minimization"
    ]
    "updatedAt" => "2023-07-10 16:36:07"
    "publicationUrl" => "https://doi.org/10.1016/j.spa.2022.07.002"
    "publicationInfo" => array:3 [
      "pages" => "452-485"
      "volume" => "152"
      "number" => ""
    ]
    "type" => array:2 [
      "fr" => "Articles"
      "en" => "Journal articles"
    ]
    "support_type" => array:2 [
      "fr" => "Revue scientifique"
      "en" => "Scientific journal"
    ]
    "countries" => array:2 [
      "fr" => null
      "en" => null
    ]
    "abstract" => array:2 [
      "fr" => "We introduce a class of Markov chains that includes models of stochastic approximation by averaging and non-averaging. Using a martingale approximation method, we establish various deviation inequalities for separately Lipschitz functions of such a chain, with different moment conditions on some dominating random variables of martingale differences. Finally, we apply these inequalities to stochastic approximation by averaging and empirical risk minimization."
      "en" => "We introduce a class of Markov chains that includes models of stochastic approximation by averaging and non-averaging. Using a martingale approximation method, we establish various deviation inequalities for separately Lipschitz functions of such a chain, with different moment conditions on some dominating random variables of martingale differences. Finally, we apply these inequalities to stochastic approximation by averaging and empirical risk minimization."
    ]
    "authors_fields" => array:2 [
      "fr" => "Systèmes d’Information, Sciences de la Décision et Statistiques"
      "en" => "Information Systems, Decision Sciences and Statistics"
    ]
    "indexedAt" => "2024-04-19T21:22:00.000Z"
    "docTitle" => "Deviation inequalities for stochastic approximation by averaging"
    "docSurtitle" => "Journal articles"
    "authorNames" => "<a href="/cv/alquier-pierre">ALQUIER Pierre</a>, FAN Xiequan, DOUKHAN Paul"
    "docDescription" => "<span class="document-property-authors">ALQUIER Pierre, FAN Xiequan, DOUKHAN Paul</span><br><span class="document-property-authors_fields">Information Systems, Decision Sciences and Statistics</span> | <span class="document-property-year">2022</span>"
    "keywordList" => "<a href="#">Deviation inequalities</a>, <a href="#">Martingales</a>, <a href="#">Iterated random functions</a>, <a href="#">Stochastic approximation by averaging</a>, <a href="#">Empirical risk minimization</a>"
    "docPreview" => "<b>Deviation inequalities for stochastic approximation by averaging</b><br><span>2022-10 | Journal articles </span>"
    "docType" => "research"
    "publicationLink" => "<a href="https://doi.org/10.1016/j.spa.2022.07.002" target="_blank">Deviation inequalities for stochastic approximation by averaging</a>"
  ]
  +lang: "en"
  +"_type": "_doc"
  +"_score": 8.615988
  +"parent": null
}