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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:A Machine Learning Framework for High-Dimensional
Mean Field Games and Optimal Control - Lars Ruthot
to (Emory University)
DTSTART;TZID=Europe/London:20211116T160000
DTEND;TZID=Europe/London:20211116T163000
UID:TALK165415AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/165415
DESCRIPTION:We consider the numerical solution of mean field g
ames and optimal control problems whose state spac
e dimension is in the tens or hundreds. In this se
tting\, most existing numerical solvers are affect
ed by the curse of dimensionality (CoD). To mitiga
te the CoD\, we present a machine learning framewo
rk that combines the approximation power of neural
networks with the scalability of Lagrangian PDE s
olvers. Specifically\, we parameterize the value f
unction with a neural network and train its weight
s using the objective function with additional pen
alties that enforce the Hamilton Jacobi Bellman eq
uations. A key benefit of this approach is that no
training data is needed\, e.g.\, no numerical sol
utions to the problem need to be computed before t
raining.\nWe illustrate our approach and its effic
acy using numerical experiments. To show the frame
work's generality\, we consider applications such
as optimal transport\, deep generative modeling\,
mean field games for crowd motion\, and multi-agen
t optimal control.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:
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