# Dynamical low-rank approximations of solutions to the Hamilton-Jacobi-Bellman equation

arXiv: https://arxiv.org/abs/2111.14540 · HTML: https://mlsanity.com/paper/2111.14540/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Nov 2021.

## Built on by (most cited first, 2 of 2)

- [Generative Modelling with Tensor Train approximations of Hamilton--Jacobi--Bellman equations](https://mlsanity.com/paper/2402.15285/) (2024)
- [Sampling from Boltzmann densities with physics informed low-rank formats](https://mlsanity.com/paper/2412.07637/) (2024)

## Abstract (arXiv)

We present a novel method to approximate optimal feedback laws for nonlinear optimal control based on low-rank tensor train (TT) decompositions. The approach is based on the Dirac-Frenkel variational principle with the modification that the optimisation uses an empirical risk. Compared to current state-of-the-art TT methods, our approach exhibits a greatly reduced computational burden while achieving comparable results. A rigorous description of the numerical scheme and demonstrations of its performance are provided.