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UID:20250723T113941EDT-2600eRivec@132.216.98.100
DTSTAMP:20250723T153941Z
DESCRIPTION:Speaker: Ruimeng Hu – University of California\, Santa Barbara\
 , United States \n\n \n	\n\n	Abstract: In this talk\, we first propose a new
  class of metrics and show that under such metrics\, the convergence of em
 pirical measures in high dimensions is free of the curse of dimensionality
 \, in contrast to Wasserstein distance. Proposed metrics are the integral 
 probability metrics\, where we propose criteria for test function spaces. 
 Examples include RKHS\, Barron space\, and flow-induced function spaces. O
 ne application studies the construction of Nash equilibrium for the homoge
 neous n-player game by its mean-field limit (mean-field game). Another app
 lication is to show the ability to overcome curves of dimensionality of de
 ep learning algorithms\, for example\, in solving Mckean-Vlasov forward-ba
 ckward stochastic differential equations with general distribution depende
 nce. This is joint work with Jiequn Han and Jihao Long\n\n	Biography: Ruime
 ng Hu is an assistant professor jointly appointed by the Department of Mat
 hematics\, and Department of Applied Probability and Statistics\, at the U
 niversity of California\, Santa Barbara (UCSB)\, USA. Her research include
 s machine learning\, financial mathematics\, game theory\, portfolio optim
 ization\, and sequential experimental design. Her research is currently su
 pported by an NSF grant as PI\, the Regents' Junior Faculty Award\, Early 
 Career Faculty Acceleration Funding by UCSB. She has submitted and publish
 ed 20+ papers in top journals including Mathematical Finance\, Notices of 
 AMS\, ICML\, SIAM Journal on Control and Optimization\, and SIAM Journal o
 n Financial Mathematics. Ruimeng Hu obtained her Ph.D. at the Department o
 f Applied Probability and Statistics at UCSB in 2018\, and B.S. in Pure an
 d Applied Mathematics at Peking University\, China in 2012.\n\n
DTSTART:20221028T180000Z
DTEND:20221028T190000Z
LOCATION:CA\, ZOOM
SUMMARY:Convergence of Empirical Measures\, Mean-Field Games and Deep Learn
 ing Algorithms
URL:/cim/channels/event/convergence-empirical-measures
 -mean-field-games-and-deep-learning-algorithms-351656
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