# A Generalized Markov-Chain Modelling Approach to $(1,\lambda )$-ES Linear Optimization: Technical Report

1 TAO - Machine Learning and Optimisation
LRI - Laboratoire de Recherche en Informatique, UP11 - Université Paris-Sud - Paris 11, Inria Saclay - Ile de France, CNRS - Centre National de la Recherche Scientifique : UMR8623
Abstract : Several recent publications investigated Markov-chain modelling of linear optimization by a $(1,\lambda )$-ES, considering both unconstrained and linearly constrained optimization, and both constant and varying step size. All of them assume normality of the involved random steps, and while this is consistent with a black-box scenario, information on the function to be optimized (e.g. separability) may be exploited by the use of another distribution. The objective of our contribution is to complement previous studies realized with normal steps, and to give sufficient conditions on the distribution of the random steps for the success of a constant step-size $(1,\lambda)$-ES on the simple problem of a linear function with a linear constraint. The decomposition of a multidimensional distribution into its marginals and the copula combining them is applied to the new distributional assumptions, particular attention being paid to distributions with Archimedean copulas.
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Cited literature [16 references]

https://hal.inria.fr/hal-01003015
Contributor : Alexandre Chotard <>
Submitted on : Tuesday, June 17, 2014 - 1:00:03 AM
Last modification on : Thursday, April 5, 2018 - 12:30:12 PM
Long-term archiving on : Wednesday, September 17, 2014 - 10:45:12 AM

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### Identifiers

• HAL Id : hal-01003015, version 2
• ARXIV : 1406.4619

### Citation

Alexandre Chotard, Martin Holena. A Generalized Markov-Chain Modelling Approach to $(1,\lambda )$-ES Linear Optimization: Technical Report. [Research Report] 2014. ⟨hal-01003015v2⟩

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