Black-Box Approximation and Optimization with Hierarchical Tucker Decomposition
This work addresses the challenge of high-dimensional optimization and approximation for researchers and practitioners in fields like computational science, offering a novel method that improves upon existing tensor-based techniques.
The authors tackled the problem of multidimensional black-box approximation and gradient-free optimization by developing HTBB, a method based on hierarchical Tucker decomposition with MaxVol indices selection, which demonstrated robustness for dimensions up to 1000 and significantly outperformed classical gradient-free methods and tensor train-based approaches in accuracy across 14 complex model problems.
We develop a new method HTBB for the multidimensional black-box approximation and gradient-free optimization, which is based on the low-rank hierarchical Tucker decomposition with the use of the MaxVol indices selection procedure. Numerical experiments for 14 complex model problems demonstrate the robustness of the proposed method for dimensions up to 1000, while it shows significantly more accurate results than classical gradient-free optimization methods, as well as approximation and optimization methods based on the popular tensor train decomposition, which represents a simpler case of a tensor network.