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dc.contributor.authorJasra, Ajay
dc.contributor.authorHeng, Jeremy
dc.contributor.authorXu, Yaxian
dc.contributor.authorBishop, Adrian N.
dc.date.accessioned2020-12-14T11:30:37Z
dc.date.available2019-12-29T13:47:31Z
dc.date.available2020-01-13T12:38:09Z
dc.date.available2020-12-14T11:30:37Z
dc.date.issued2020-12-03
dc.date.submitted2020-02-05
dc.identifier.citationJasra, A., Heng, J., Xu, Y., & Bishop, A. N. (2020). A multilevel approach for stochastic nonlinear optimal control. International Journal of Control, 1–15. doi:10.1080/00207179.2020.1849805
dc.identifier.issn1366-5820
dc.identifier.issn0020-7179
dc.identifier.doi10.1080/00207179.2020.1849805
dc.identifier.urihttp://hdl.handle.net/10754/660859
dc.description.abstractWe 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 (Formula presented.) mean squared error with a cost of (Formula presented.). In contrast, a cost of (Formula presented.) is required for the existing methodology to achieve the same mean squared error. Our approach is illustrated on two numerical examples.
dc.description.sponsorshipA.J. and Y.X. were supported by an AcRF tier 2 [grant number R-155-000-161-112]. A.J. is affiliated with the Risk Management Institute, the Center for Quantitative Finance and the OR & Analytics cluster at NUS. A.J. was supported by a KAUST CRG4 grant ref: 2584
dc.publisherInforma UK Limited
dc.relation.urlhttps://www.tandfonline.com/doi/full/10.1080/00207179.2020.1849805
dc.rightsArchived with thanks to International Journal of Control
dc.titleA multilevel approach for stochastic nonlinear optimal control
dc.typeArticle
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.identifier.journalInternational Journal of Control
dc.rights.embargodate2021-12-03
dc.eprint.versionPost-print
dc.contributor.institutionESSEC Business School, Singapore, Singapore
dc.contributor.institutionDepartment of Statistics Applied Probability, National University of Singapore, Singapore, Singapore
dc.contributor.institutionUniversity of Technology Sydney, Sydney, Australia
dc.identifier.pages1-15
dc.identifier.arxivid1901.05583
kaust.personJasra, Ajay
kaust.grant.numberCRG4 grant ref: 2584
dc.date.accepted2020-11-03
dc.identifier.eid2-s2.0-85097089529
refterms.dateFOA2019-12-29T13:48:08Z


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