Essec\Faculty\Model\Contribution {#2216
  #_index: "academ_contributions"
  #_id: "11159"
  #_source: array:26 [
    "id" => "11159"
    "slug" => "a-multilevel-approach-for-stochastic-nonlinear-optimal-control"
    "yearMonth" => "2022-05"
    "year" => "2022"
    "title" => "A Multilevel Approach for Stochastic Nonlinear Optimal Control"
    "description" => "JASRA, A., HENG, J., XU, Y. et BISHOP, A.N. (2022). A Multilevel Approach for Stochastic Nonlinear Optimal Control. <i>International Journal of Control</i>, 95(5), pp. 1290-1304."
    "authors" => array:3 [
      0 => array:3 [
        "name" => "HENG Jeremy"
        "bid" => "B00760223"
        "slug" => "heng-jeremy"
      ]
      1 => array:1 [
        "name" => "XU Yaxian"
      ]
      2 => array:1 [
        "name" => "BISHOP Adrian N."
      ]
    ]
    "ouvrage" => ""
    "keywords" => array:4 [
      0 => "optimal control"
      1 => "multilevel Monte Carlo"
      2 => "Markov chain Monte Carlo"
      3 => "sequential  Monte Carlo"
    ]
    "updatedAt" => "2023-07-10 17:17:38"
    "publicationUrl" => "https://www.tandfonline.com/doi/abs/10.1080/00207179.2020.1849805?journalCode=tcon20"
    "publicationInfo" => array:3 [
      "pages" => "1290-1304"
      "volume" => "95"
      "number" => "5"
    ]
    "type" => array:2 [
      "fr" => "Articles"
      "en" => "Journal articles"
    ]
    "support_type" => array:2 [
      "fr" => "Revue scientifique"
      "en" => "Scientific journal"
    ]
    "countries" => array:2 [
      "fr" => "Royaume-Uni"
      "en" => "United Kingdom"
    ]
    "abstract" => array:2 [
      "fr" => "We consider a class of finite-time horizon nonlinear stochastic optimal control problem. Although the optimal control admits a path integral representation for this class of control problems, efficient computation of the associated path integrals remains a challenging task. We propose a new Monte Carlo approach that significantly improves upon existing methodology. We tackle the issue of exponential growth in variance with the time horizon by casting optimal control estimation as a smoothing problem for a state-space model, and applying smoothing algorithms based on particle Markov chain Monte Carlo. To further reduce the cost, we then develop a multilevel Monte Carlo method which allows us to obtain an estimator of the optimal control with O(ϵ2) mean squared error with a cost of O(ϵ−2log(ϵ)2). In contrast, a cost of O(ϵ−3) is required for the existing methodology to achieve the same mean squared error. Our approach is illustrated on two numerical examples."
      "en" => "We consider a class of finite-time horizon nonlinear stochastic optimal control problem. Although the optimal control admits a path integral representation for this class of control problems, efficient computation of the associated path integrals remains a challenging task. We propose a new Monte Carlo approach that significantly improves upon existing methodology. We tackle the issue of exponential growth in variance with the time horizon by casting optimal control estimation as a smoothing problem for a state-space model, and applying smoothing algorithms based on particle Markov chain Monte Carlo. To further reduce the cost, we then develop a multilevel Monte Carlo method which allows us to obtain an estimator of the optimal control with O(ϵ2) mean squared error with a cost of O(ϵ−2log(ϵ)2). In contrast, a cost of O(ϵ−3) is required for the existing methodology to achieve the same mean squared error. Our approach is illustrated on two numerical examples."
    ]
    "authors_fields" => array:2 [
      "fr" => "Systèmes d'Information, Data Analytics et Opérations"
      "en" => "Information Systems, Data Analytics and Operations"
    ]
    "indexedAt" => "2024-12-22T04:21:46.000Z"
    "docTitle" => "A Multilevel Approach for Stochastic Nonlinear Optimal Control"
    "docSurtitle" => "Journal articles"
    "authorNames" => "<a href="/cv/heng-jeremy">HENG Jeremy</a>, XU Yaxian, BISHOP Adrian N."
    "docDescription" => "<span class="document-property-authors">HENG Jeremy, XU Yaxian, BISHOP Adrian N.</span><br><span class="document-property-authors_fields">Information Systems, Data Analytics and Operations</span> | <span class="document-property-year">2022</span>"
    "keywordList" => "<a href="#">optimal control</a>, <a href="#">multilevel Monte Carlo</a>, <a href="#">Markov chain Monte Carlo</a>, <a href="#">sequential  Monte Carlo</a>"
    "docPreview" => "<b>A Multilevel Approach for Stochastic Nonlinear Optimal Control</b><br><span>2022-05 | Journal articles </span>"
    "docType" => "research"
    "publicationLink" => "<a href="https://www.tandfonline.com/doi/abs/10.1080/00207179.2020.1849805?journalCode=tcon20" target="_blank">A Multilevel Approach for Stochastic Nonlinear Optimal Control</a>"
  ]
  +lang: "en"
  +"_type": "_doc"
  +"_score": 8.639127
  +"parent": null
}