Approximative Policy Iteration for Exit Time Feedback Control Problems driven by Stochastic Differential Equations using Tensor Train format
- 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.
| Author: | Konstantin FackeldeyORCiD, Mathias Oster, Leon Sallandt, Reinhold Schneider |
|---|---|
| Document Type: | Article |
| Parent Title (English): | SIAM Journal on Multiscale Modeling and Simulation |
| Volume: | 20 |
| Issue: | 1 |
| First Page: | 379 |
| Last Page: | 403 |
| Year of first publication: | 2022 |
| ArXiv Id: | http://arxiv.org/abs/2010.04465 |
| DOI: | https://doi.org/10.1137/20M1372500 |
