# Log-linear Convergence and Optimal Bounds for the $(1+1)$-ES

1 TANC - Algorithmic number theory for cryptology
Inria Saclay - Ile de France, LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau]
Abstract : The $(1+1)$-ES is modeled by a general stochastic process whose asymptotic behavior is investigated. Under general assumptions, it is shown that the convergence of the related algorithm is sub-log-linear, bounded below by an explicit log-linear rate. For the specific case of spherical functions and scale-invariant algorithm, it is proved using the Law of Large Numbers for orthogonal variables, that the linear convergence holds almost surely and that the best convergence rate is reached. Experimental simulations illustrate the theoretical results.
Document type :
Conference papers

Cited literature [10 references]

https://hal.inria.fr/inria-00173483
Contributor : Anne Auger <>
Submitted on : Thursday, July 3, 2008 - 2:30:27 PM
Last modification on : Wednesday, April 3, 2019 - 1:55:57 AM
Long-term archiving on: : Friday, November 25, 2016 - 11:59:04 PM

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AJL_EA07WithErrata.pdf
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### Citation

Mohamed Jebalia, Anne Auger, Pierre Liardet. Log-linear Convergence and Optimal Bounds for the $(1+1)$-ES. Evolution Artificielle, Oct 2007, Tours, France. pp.207-218, ⟨10.1007/978-3-540-79305-2⟩. ⟨inria-00173483v4⟩

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