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

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