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dc.contributor.advisorTsiotras, Panagiotis
dc.contributor.authorHawkins, Kelsey Pal
dc.date.accessioned2022-01-14T16:07:08Z
dc.date.available2022-01-14T16:07:08Z
dc.date.created2021-12
dc.date.issued2021-08-25
dc.date.submittedDecember 2021
dc.identifier.urihttp://hdl.handle.net/1853/66058
dc.description.abstractThree significant advancements are proposed for improving numerical methods in the solution of forward-backward stochastic differential equations (FBSDEs) appearing in the Feynman-Kac representation of the value function in stochastic optimal control (SOC) problems. First, we propose a novel characterization of FBSDE estimators as either on-policy or off-policy, highlighting the intuition for these techniques that the distribution over which value functions are approximated should, to some extent, match the distribution the policies generate. Second, two novel numerical estimators are proposed for improving the accuracy of single-timestep updates. In the case of LQR problems, we demonstrate both in theory and in numerical simulation that our estimators result in near machine-precision level accuracy, in contrast to previously proposed methods that can potentially diverge on the same problems. Third, we propose a new method for accelerating the global convergence of FBSDE methods. By the repeated use of the Girsanov change of probability measures, it is demonstrated how a McKean-Markov branched sampling method can be utilized for the forward integration pass, as long as the controlled drift terms are appropriately compensated in the backward integration pass. Subsequently, a numerical approximation of the value function is proposed by solving a series of function approximation problems backwards in time along the edges of a space-filling tree.
dc.format.mimetypeapplication/pdf
dc.language.isoen_US
dc.publisherGeorgia Institute of Technology
dc.subjectStochastic optimal control
dc.subjectForward-backward stochastic differential equations
dc.subjectRobotics
dc.subjectPartial differential equations
dc.subjectMotion planning
dc.subjectRapidly exploring random trees
dc.titleFeynman-Kac Numerical Techniques for Stochastic Optimal Control
dc.typeDissertation
dc.description.degreePh.D.
dc.contributor.departmentInteractive Computing
thesis.degree.levelDoctoral
dc.contributor.committeeMemberBerenson, Dmitry
dc.contributor.committeeMemberCoogan, Samuel
dc.contributor.committeeMemberTheodorou, Evangelos
dc.contributor.committeeMemberVamvoudakis, Kyriakos
dc.date.updated2022-01-14T16:07:09Z


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