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

Abstract

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.