# Approximative Policy Iteration for Exit Time Feedback Control Problems driven by Stochastic Differential Equations using Tensor Train format

arXiv: https://arxiv.org/abs/2010.04465 · HTML: https://mlsanity.com/paper/2010.04465/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Oct 2020.

## Built on by (most cited first, 4 of 4)

- [Solving high-dimensional parabolic PDEs using the tensor train format](https://mlsanity.com/paper/2102.11830/) (2021)
- [From continuous-time formulations to discretization schemes: tensor trains and robust regression for BSDEs and parabolic PDEs](https://mlsanity.com/paper/2307.15496/) (2023)
- [Convergence bounds for nonlinear least squares and applications to tensor recovery](https://mlsanity.com/paper/2108.05237/) (2021)
- [Tensor Gaussian Processes: Efficient Solvers for Nonlinear PDEs](https://mlsanity.com/paper/2510.13772/) (2025)

## Abstract (arXiv)

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.