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SUMMARY:A Machine Learning Framework for High-Dimensional Mean Field Games
  and Optimal Control - Lars Ruthotto (Emory University)
DTSTART:20211116T160000Z
DTEND:20211116T163000Z
UID:TALK165415@talks.cam.ac.uk
DESCRIPTION:We consider the numerical solution of mean field games and opt
 imal control problems whose state space dimension is in the tens or hundre
 ds. In this setting\, most existing numerical solvers are affected by the 
 curse of dimensionality (CoD). To mitigate the CoD\, we present a machine 
 learning framework that combines the approximation power of neural network
 s with the scalability of Lagrangian PDE solvers. Specifically\, we parame
 terize the value function with a neural network and train its weights usin
 g the objective function with additional penalties that enforce the Hamilt
 on Jacobi Bellman equations. A key benefit of this approach is that no tra
 ining data is needed\, e.g.\, no numerical solutions to the problem need t
 o be computed before training.\nWe illustrate our approach and its efficac
 y using numerical experiments. To show the framework's generality\, we con
 sider applications such as optimal transport\, deep generative modeling\, 
 mean field games for crowd motion\, and multi-agent optimal control.
LOCATION:Seminar Room 1\, Newton Institute
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