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Conditionning, halting criteria and choosing lambda

Olivier Teytaud 1
1 TANC - Algorithmic number theory for cryptology
Inria Saclay - Ile de France, LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau]
Abstract : We show the convergence of 1+ lambda-ES with standard step-size update-rules on a large family of fitness functions without any convexity assumption or quasi-convexity assumptions ([5, 6]). The result provides a rule for choosing lambda and shows the consistency of halting criteria based on thresholds on the step-size. The family of functions under work is defined through a conditionnumber that generalizes usual condition-numbers in a manner that only depends on level-sets. We consider that the definition of this conditionnumber 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.
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https://hal.inria.fr/inria-00173237
Contributor : Olivier Teytaud <>
Submitted on : Wednesday, September 19, 2007 - 2:36:44 PM
Last modification on : Wednesday, March 27, 2019 - 4:41:29 PM
Long-term archiving on: : Friday, April 9, 2010 - 2:29:21 AM

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Olivier Teytaud. Conditionning, halting criteria and choosing lambda. EA07, 2007, Tours, France. ⟨inria-00173237⟩

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