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Erschienen in:
2008 | OriginalPaper | Buchkapitel
Conditioning, Halting Criteria and Choosing λ
verfasst von : Olivier Teytaud
Erschienen in: Artificial Evolution
Verlag: Springer Berlin Heidelberg
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We show the convergence of 1 +
λ
-ES with standard step-size update-rules on a large family of fitness functions without any convexity assumption or quasi-convexity assumptions ([3,6]). The result provides a rule for choosing
λ
and shows the consistency of halting criteria based on thresholds on the step-size.
The family of functions under work is defined through a condition-number that generalizes usual condition-numbers in a manner that only depends on level-sets. We consider that the definition of this condition-number is the relevant one for evolutionary algorithms; in particular, global convergence results without convexity or quasi-convexity assumptions are proved when this condition-number is finite.