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SUMMARY:Convergence of Empirical Measures\, Mean-Field Games and Signature
 s - Ruimeng  Hu (University of California\, Santa Barbara)
DTSTART:20211117T160000Z
DTEND:20211117T163000Z
UID:TALK165439@talks.cam.ac.uk
DESCRIPTION:In this talk\, we first propose a new class of metrics and sho
 w that under such metrics\, the convergence of empirical measures in high 
 dimensions is free of&nbsp\;the curse&nbsp\;of dimensionality\, in contras
 t to Wasserstein distance. Proposed metrics originate from the maximum mea
 n discrepancy\, which we generalize by proposing criteria for test functio
 n spaces. Examples include RKHS\, Barron space\, and flow-induced function
  spaces. One application studies the construction of&nbsp\;Nash equilibriu
 m for the homogeneous n-player game by its mean-field limit (mean-field ga
 me). Then we discuss mean-field games with common noise and propose a deep
  learning algorithm based on fictitious play and signatures in rough path 
 theory. The first part of the work collaborates with Jiequn Han and Jihao 
 Long\; the second part is the joint work with a Ph.D. student Ming Min at 
 UCSB.&nbsp\;
LOCATION:Seminar Room 1\, Newton Institute
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