# -cancelled- Variational Monte Carlo Methods for Classical Solution of Hamilton Jacobi Bellmann Equations

Reinhold Schneider, TU Berlin, Germany 2.28.0.10810:15 - 11:15

*- Unfortunatly this colloquium will be cancelled due to the current situation concering the Corona Virus -*

Suppose the PDE is cast in a variational form, in Variational Monte

Carlo we replace the original objective functional by an empirical func-

tional in a similar way as for the quadratic loss functions in regression

and statistical learning.

As an application computing an approximation a classical solu-

tion of the non-linear and high-dimensional (stationary) Hamilton Bell-

mann equations subordinated to an in nite horizon feedback control

problem. Variational Monte Carlo method are used to solve an inhomo-

geneous backward Kolmogorov equation inside a policy iteration step.

We use multi-polynomial ansatz-functions and HT tensor product to

represent the solution and circumventing the curse of dimensions (deep

neural networks and other tools from ML may be used alternatively).

We show improvement over LQR (linear quadratic regulator) used in

engineering.

invited by Sebastian Reich