TY - JOUR A1 - Fackeldey, Konstantin A1 - Oster, Mathias A1 - Sallandt, Leon A1 - Schneider, Reinhold T1 - Approximative Policy Iteration for Exit Time Feedback Control Problems driven by Stochastic Differential Equations using Tensor Train format T2 - SIAM Journal on Multiscale Modeling and Simulation N2 - 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. Y1 - 2022 UR - https://opus4.kobv.de/opus4-zib/frontdoor/index/index/docId/7983 VL - 20 IS - 1 SP - 379 EP - 403 ER -