Conditioning, halting criteria and choosing lambda
Olivier Teytaud
In: EA07(2007).

Abstract

Abstract. 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 assump- tions are proved when this condition-number is finite.

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