{"649075":{"#nid":"649075","#data":{"type":"event","title":"PhD Defense by Kelsey Hawkins","body":[{"value":"\u003Cp\u003E\u003Cstrong\u003ETitle: \u003C\/strong\u003EFeynman-Kac Numerical Techniques for Stochastic Optimal Control\u003C\/p\u003E\r\n\r\n\u003Cp\u003E\u0026nbsp;\u003C\/p\u003E\r\n\r\n\u003Cp\u003E\u003Cstrong\u003EDate\u003C\/strong\u003E: Monday, August 9th, 2021\u003C\/p\u003E\r\n\r\n\u003Cp\u003E\u003Cstrong\u003ETime\u003C\/strong\u003E: 11:00 AM - 1:00 PM (EDT)\u003C\/p\u003E\r\n\r\n\u003Cp\u003E\u003Cstrong\u003ELocation:\u0026nbsp;\u003C\/strong\u003EBlueJeans meeting (\u003Ca href=\u0022https:\/\/bluejeans.com\/303268392\/2685\u0022\u003Ehttps:\/\/bluejeans.com\/303268392\/2685\u003C\/a\u003E)\u003C\/p\u003E\r\n\r\n\u003Cp\u003E\u0026nbsp;\u003C\/p\u003E\r\n\r\n\u003Cp\u003E\u003Cstrong\u003EKelsey\u003C\/strong\u003E\u003Cstrong\u003E\u0026nbsp;Hawkins\u003C\/strong\u003E\u003C\/p\u003E\r\n\r\n\u003Cp\u003ERobotics Ph.D. Candidate\u003C\/p\u003E\r\n\r\n\u003Cp\u003EInstitute for Robotics and Intelligent Machines\u003C\/p\u003E\r\n\r\n\u003Cp\u003EGeorgia Institute of Technology\u003C\/p\u003E\r\n\r\n\u003Cp\u003E\u003Cstrong\u003ECommittee:\u003C\/strong\u003E\u003C\/p\u003E\r\n\r\n\u003Cp\u003EDr. Panos Tsiotras (Advisor) \u0026ndash; School of Aerospace Engineering, Georgia Tech\u003C\/p\u003E\r\n\r\n\u003Cp\u003EDr. Dmitry Berenson \u0026ndash; Electrical Engineering and Computer Science Dept., University of Michigan\u003C\/p\u003E\r\n\r\n\u003Cp\u003EDr. Sam Coogan \u0026ndash; School of Electrical and Computer Engineering, Georgia Tech\u003C\/p\u003E\r\n\r\n\u003Cp\u003EDr. Evangelos Theodorou \u0026ndash; School of\u0026nbsp;Aerospace Engineering, College of Computing, Georgia Tech\u003C\/p\u003E\r\n\r\n\u003Cp\u003EDr. Kyriakos Vamvoudakis \u0026ndash;\u0026nbsp;School of\u0026nbsp;Aerospace Engineering,\u0026nbsp;Georgia Tech\u003C\/p\u003E\r\n\r\n\u003Cp\u003E\u0026nbsp;\u003C\/p\u003E\r\n\r\n\u003Cp\u003E\u003Cstrong\u003EAbstract:\u003C\/strong\u003E\u003C\/p\u003E\r\n\r\n\u003Cp\u003EThree 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.\u003C\/p\u003E\r\n\r\n\u003Cp\u003E\u0026nbsp;\u003C\/p\u003E\r\n\r\n\u003Cp\u003ESecond, 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.\u003C\/p\u003E\r\n\r\n\u003Cp\u003E\u0026nbsp;\u003C\/p\u003E\r\n\r\n\u003Cp\u003EThird, 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. \u0026nbsp;\u003C\/p\u003E\r\n\r\n\u003Cp\u003E\u0026nbsp;\u003C\/p\u003E\r\n","summary":null,"format":"limited_html"}],"field_subtitle":"","field_summary":"","field_summary_sentence":[{"value":"Feynman-Kac Numerical Techniques for Stochastic Optimal Control"}],"uid":"27707","created_gmt":"2021-07-27 13:50:39","changed_gmt":"2021-07-27 13:50:39","author":"Tatianna Richardson","boilerplate_text":"","field_publication":"","field_article_url":"","field_event_time":{"event_time_start":"2021-08-09T12:00:00-04:00","event_time_end":"2021-08-09T14:00:00-04:00","event_time_end_last":"2021-08-09T14:00:00-04:00","gmt_time_start":"2021-08-09 16:00:00","gmt_time_end":"2021-08-09 18:00:00","gmt_time_end_last":"2021-08-09 18:00:00","rrule":null,"timezone":"America\/New_York"},"extras":[],"groups":[{"id":"221981","name":"Graduate Studies"}],"categories":[],"keywords":[{"id":"100811","name":"Phd Defense"}],"core_research_areas":[],"news_room_topics":[],"event_categories":[{"id":"1788","name":"Other\/Miscellaneous"}],"invited_audience":[{"id":"78761","name":"Faculty\/Staff"},{"id":"78771","name":"Public"},{"id":"174045","name":"Graduate students"},{"id":"78751","name":"Undergraduate students"}],"affiliations":[],"classification":[],"areas_of_expertise":[],"news_and_recent_appearances":[],"phone":[],"contact":[],"email":[],"slides":[],"orientation":[],"userdata":""}}}