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SUMMARY:Solving Fully Coupled FBSDEs and Stochastic Hamiltonian Systems vi
 a Deep Learning - Ying Peng (Shandong University)
DTSTART:20211116T113000Z
DTEND:20211116T120000Z
UID:TALK165400@talks.cam.ac.uk
DESCRIPTION:In this talk\, I will present our recent results on numerical 
 solution of high-dimensional Forward backward Stochastic Differential Equa
 tions (FBSDEs) and stochastic control problems via deep learning.In the fi
 eld of numerically solving BSDEs\, a well-known challenging problem was "t
 he curse of dimensionality". A recent important breakthrough in this resea
 rch direction was made by E et al by using deep neural network.\nIn this t
 alk\, we present a type of fully coupled high dimensional FBSDE in which t
 he drift and diffusion coefficient are all given (nonlinear) functions of 
 the backward variables (Y\,Z). In order to solve this type of FBSDE\, we s
 ystematically explore the dependence of the term $Z$ on state precesses $X
 \,Y$ and even $Z$ itself. Three algorithms corresponding to different kind
 s of state feedback are developed via deep neural network and the numerica
 l results demonstrate a remarkable performance. It is worth to notice that
  how to provide an efficient algorithm for this type of fully coupled nonl
 inear FBSDE was a largely open problem.The well-known nonlinear stochastic
  Hamiltonian system is a typical example of FBSDEs through which our algor
 ithms have been successfully applied. We have also developed a direct stoc
 hastic optimal control approach for solving numerically this high dimensio
 nal problem. Two different algorithms suitable for different cases of the 
 control problem are proposed. The numerical results demonstrate more stabl
 e convergence comparing with the FBSDE method for different Hamiltonian sy
 stems.Inspired by the deep learning method for solving FBSDEs\, we also pr
 opose a method to solve high dimensional stochastic optimal control proble
 m from the view of the stochastic maximum principle.Joint work with Prof. 
 Shaolin Ji\, Shige Peng and Dr. Xichuan Zhang.
LOCATION:Seminar Room 1\, Newton Institute
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