WIAS Preprint No. 2896, (2021)

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


  • Eigel, Martin
  • Schneider, Reinhold
  • Sommer, David
    ORCID: 0000-0002-6797-8009

2020 Mathematics Subject Classification

  • 49L20 49M37 93-08 93B52 15A69


  • Dynamical low-rank approximation, feedback control, Hamilton-Jacobi-Bellman, variational Monte Carlo, tensor product approximation




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

Appeared in

  • Numer. Linear Algebra Appl., 30 (2023), pp. e2463/1--e2463/20 (published online on 03.08.2022), DOI 10.1002/nla.2463 .

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