A dimensionality reduction technique for unconstrained global optimization of functions with low effective dimensionality

Coralia Cartis, Adilet Otemissov

Research output: Contribution to journalArticlepeer-review

Abstract

We investigate the unconstrained global optimization of functions with low effective dimensionality, which are constant along certain (unknown) linear subspaces. Extending the technique of random subspace embeddings in Wang et al. (2016, J. Artificial Intelligence Res., 55, 361-387), we study a generic Random Embeddings for Global Optimization (REGO) framework that is compatible with any global minimization algorithm. Instead of the original, potentially large-scale optimization problem, within REGO, a Gaussian random, low-dimensional problem with bound constraints is formulated and solved in a reduced space. We provide novel probabilistic bounds for the success of REGO in solving the original, low effective-dimensionality problem, which show its independence of the (potentially large) ambient dimension and its precise dependence on the dimensions of the effective and embedding subspaces. These results significantly improve existing theoretical analyses by providing the exact distribution of a reduced minimizer and its Euclidean norm and by the general assumptions required on the problem. We validate our theoretical findings by extensive numerical testing of REGO with three types of global optimization solvers, illustrating the improved scalability of REGO compared with the full-dimensional application of the respective solvers.

Original languageEnglish
Pages (from-to)167-201
Number of pages35
JournalInformation and Inference
Volume11
Issue number1
DOIs
Publication statusPublished - Mar 1 2022
Externally publishedYes

Keywords

  • dimensionality reduction techniques
  • functions with low effective dimensionality
  • global optimization
  • random matrix theory

ASJC Scopus subject areas

  • Analysis
  • Statistics and Probability
  • Numerical Analysis
  • Computational Theory and Mathematics
  • Applied Mathematics

Fingerprint

Dive into the research topics of 'A dimensionality reduction technique for unconstrained global optimization of functions with low effective dimensionality'. Together they form a unique fingerprint.

Cite this