  We consider a stochastic optimal exit time feedback control problem. The
Bellman equation is solved approximatively via the Policy Iteration algorithm
on a polynomial ansatz space by a sequence of linear equations. As high degree
multi-polynomials are needed, the corresponding equations suffer from the curse
of dimensionality even in moderate dimensions. We employ tensor-train methods
to account for this problem. The approximation process within the Policy
Iteration is done via a Least-Squares ansatz and the integration is done via
Monte-Carlo methods. Numerical evidences are given for the (multi dimensional)
double well potential and a three-hole potential.
