Geometric Convergence and Concentration Inequalities for the Feynman–Kac Genetic Algorithm

In this paper, we consider a genetic evolution model associated to a given Feynman–Kac flow (called also the simple genetic algorithm). We first obtain an estimate of the contraction coefficient of this interacting particle system in some suitable metric, independent of the number of particles in th...

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Bibliographic Details
Published inFrontiers of Mathematics Vol. 19; no. 2; pp. 321 - 334
Main Authors Del Moral, Pierre, Wang, Xinyu
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.03.2024
Springer Nature B.V
Springer Verlag
Subjects
Convergence
Genetic algorithms
Inequalities
Mathematics
Mathematics and Statistics
Research Article
Statistics
60E15
neutral evolution
39B62
Concentration inequality
Feynman–Kac model
mean field particle model
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ISSN2731-8648
1673-3452
2731-8656
2731-8656
1673-3576
DOI10.1007/s11464-022-0089-z

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Summary:In this paper, we consider a genetic evolution model associated to a given Feynman–Kac flow (called also the simple genetic algorithm). We first obtain an estimate of the contraction coefficient of this interacting particle system in some suitable metric, independent of the number of particles in the system. Second, by transport-entropy inequality technique, we obtain some concentration inequalities for the particle system, uniform in time and in the number of particles.
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ISSN:2731-8648
1673-3452
2731-8656
2731-8656
1673-3576
DOI:10.1007/s11464-022-0089-z