Skip to Main content Skip to Navigation
Conference papers

On the codimension of the set of optima: large scale optimisation with few relevant variables

Vincent Berthier 1, 2 Olivier Teytaud 1, 2 
2 TAO - Machine Learning and Optimisation
LRI - Laboratoire de Recherche en Informatique, UP11 - Université Paris-Sud - Paris 11, Inria Saclay - Ile de France, CNRS - Centre National de la Recherche Scientifique : UMR8623
Abstract : The complexity of continuous optimisation by comparison-based algorithms has been developed in several recent papers.Roughly speaking, these papers conclude that a precision can be reached with cost Θ(n log(1//)) in dimension n within polylogarithmic factors for the sphere function. Compared to other (non comparison-based) algorithms, this rate is not excellent; on the other hand, it is classically considered that comparison-based algorithms have some robustness advantages, as well as scalability on parallel machines and simplicity. In the present paper we show another advantage, namely resilience to useless variables, thanks to a complexity bound Θ(m log(1//)) where m is the codimension of the set of optima, possibly m << n. In addition, experiments show that some evolutionary algorithms have a negligible computational complexity even in high dimension, making them practical for huge problems with many useless variables.
Complete list of metadata

Cited literature [44 references]  Display  Hide  Download
Contributor : Olivier Teytaud Connect in order to contact the contributor
Submitted on : Monday, September 7, 2015 - 10:44:39 AM
Last modification on : Saturday, June 25, 2022 - 10:17:28 PM
Long-term archiving on: : Tuesday, December 8, 2015 - 11:08:30 AM


Files produced by the author(s)


  • HAL Id : hal-01194519, version 1


Vincent Berthier, Olivier Teytaud. On the codimension of the set of optima: large scale optimisation with few relevant variables. Artificial Evolution 2015, 2015, Lyon, France. To appear. ⟨hal-01194519⟩



Record views


Files downloads