Essec\Faculty\Model\Contribution {#6196`
#_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, Sciences de la Décision et Statistiques"
"en" => "Information Systems, Decision Sciences and Statistics"
`]
"indexedAt" => "2024-02-27T07:21:46.000Z"
"docTitle" => "A Multilevel Approach for Stochastic Nonlinear Optimal Control"
"docSurtitle" => "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">Systèmes d’Information, Sciences de la Décision et Statistiques</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 | 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: "fr"
+"_type": "_doc"
+"_score": 8.789477
+"parent": null
}