Riemannian Optimization for Solving High-Dimensional Problems with Low-Rank Tensor Structure

Steinlechner, Michael

doi:10.5075/epfl-thesis-6958

Search citation statements

Order By: Relevance

Paper Sections

Select...

Introduction1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2017

2022

Publication Types

Select...

Article2

Relationship

Self Cite0

Independent2

Authors

Journals

Cited by 2 publications

(1 citation statement)

References 62 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…With appropriate modifications, this approach can already be combined with regression techniques performed for example, by machine learning methods, in particular artificial neural networks (NN). In the present paper, we follow a different approach, exploiting the Riemannian structure of the TT manifold 8,9 by an empirical version of the Dirac-Frenkel principle.…”

Section: Introductionmentioning

confidence: 99%

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

Eigel

Schneider

Sommer

2022

Numerical Linear Algebra App

View full text Add to dashboard Cite

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 optimization 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.

show abstract

Section: Introductionmentioning

confidence: 99%