# Lower bounds for evolution strategies using VC-dimension

2 TAO - Machine Learning and Optimisation
CNRS - Centre National de la Recherche Scientifique : UMR8623, Inria Saclay - Ile de France, UP11 - Université Paris-Sud - Paris 11, LRI - Laboratoire de Recherche en Informatique
Abstract : We derive lower bounds for comparison-based or selection-based algorithms, improving existing results in the continuous setting, and extending them to non-trivial results in the discrete case. We introduce for that the use of the VC-dimension of the level sets of the fitness functions; results are then obtained through the use of Sauer's lemma. In the special case of optmization of the sphere function, improved lower bounds are obtained by bounding the possible number of sign conditions realized by some systems of equations. The results include several applications to the parametrization of sequential or parallel algorithms of type $\mul$-ES.
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Conference papers

Cited literature [20 references]

https://hal.inria.fr/inria-00287845
Contributor : Olivier Teytaud <>
Submitted on : Friday, June 13, 2008 - 10:09:57 AM
Last modification on : Thursday, July 8, 2021 - 3:47:44 AM
Long-term archiving on: : Friday, September 28, 2012 - 3:52:45 PM

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paralb.pdf
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• HAL Id : inria-00287845, version 1

### Citation

Olivier Teytaud, Hervé Fournier. Lower bounds for evolution strategies using VC-dimension. Parallel Problem Solving from Nature, Sep 2008, Dortmund, Germany. 10 p. ⟨inria-00287845⟩

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