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DESCRIPTION:Title: Convergence of Empirical Measures\, Mean-Field Games and
  Deep Learning Algorithms.\n\nAbstract: In this talk\, we first propose a 
 new class of metrics and show that under such metrics\, the convergence of
  empirical measures in high dimensions is free of the curse of dimensional
 ity\, in contrast to Wasserstein distance. Proposed metrics are the integr
 al probability metrics\, where we propose criteria for test function space
 s. Examples include RKHS\, Barron space\, and flow-induced function spaces
 . One application studies the construction of Nash equilibrium for the hom
 ogeneous n-player game by its mean-field limit (mean-field game). Another 
 application is to show the ability to overcome curves of dimensionality of
  deep learning algorithms\, for example\, in solving Mckean-Vlasov forward
 -backward stochastic differential equations with general distribution depe
 ndence. This is joint work with Jiequn Han and Jihao Long. Résumé In this 
 talk\, we first propose a new class of metrics and show that under such me
 trics\, the convergence of empirical measures in high dimensions is free o
 f the curse of dimensionality\, in contrast to Wasserstein distance. Propo
 sed metrics are the integral probability metrics\, where we propose criter
 ia for test function spaces. Examples include RKHS\, Barron space\, and fl
 ow-induced function spaces. One application studies the construction of Na
 sh equilibrium for the homogeneous n-player game by its mean-field limit (
 mean-field game). Another application is to show the ability to overcome c
 urves of dimensionality of deep learning algorithms\, for example\, in sol
 ving Mckean-Vlasov forward-backward stochastic differential equations with
  general distribution dependence. This is joint work with Jiequn Han and J
 ihao Long.\n\nZoom Lecture \n\nhttp://www.crm.umontreal.ca/cal/en/%0A%20ht
 tp://quantact.uqam.ca/\n
DTSTART:20220916T190000Z
DTEND:20220916T200000Z
SUMMARY:Ruimeng Lu\, UC Santa Barbara
URL:/mathstat/channels/event/ruimeng-lu-uc-santa-barba
 ra-341774
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