On the choice of the low-dimensional domain for global optimization via random embeddings

Abstract : The challenge of taking many variables into account in optimization problems may be overcome under the hypothesis of low effective dimensionality. Then, the search of solutions can be reduced to the random embedding of a low dimensional space into the original one, resulting in a more manageable optimization problem. Specifically, in the case of time consuming black-box functions and when the budget of evaluations is severely limited, global optimization with random embeddings appears as a sound alternative to random search. Yet, in the case of box constraints on the native variables, defining suitable bounds on a low dimensional domain appears to be complex. Indeed, a small search domain does not guarantee to find a solution even under restrictive hypotheses about the function, while a larger one may slow down convergence dramatically. Here we tackle the issue of low-dimensional domain selection based on a detailed study of the properties of the random embedding, giving insight on the aforementioned difficulties. In particular, we describe a minimal low-dimensional set in correspondence with the embedded search space. We additionally show that an alternative equivalent embedding procedure yields simultaneously a simpler definition of the low-dimensional minimal set and better properties in practice. Finally, the performance and robustness gains of the proposed enhancements for Bayesian optimization are illustrated on three examples.
Liste complète des métadonnées

https://hal.inria.fr/hal-01508196
Contributeur : Mickaël Binois <>
Soumis le : vendredi 14 avril 2017 - 02:57:41
Dernière modification le : mercredi 13 septembre 2017 - 10:13:12
Document(s) archivé(s) le : samedi 15 juillet 2017 - 12:24:01

Fichiers

OnTheChoice.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

  • HAL Id : hal-01508196, version 1
  • ARXIV : 1704.05318

Citation

Mickaël Binois, David Ginsbourger, Olivier Roustant. On the choice of the low-dimensional domain for global optimization via random embeddings. 2017. <hal-01508196>

Partager

Métriques

Consultations de
la notice

170

Téléchargements du document

38