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Keywords
(14)
Continuous Optimization
Convergence Rate
Evolution Strategy
Linear Convergence
Mathematical Analysis
Multiplicative Noise
Numerical Optimization
Objective Function
Scale Invariance
Search Method
Stochastic Optimization
Stochastic Search
Theoretical Foundation
Markov Chain
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LogLinear Convergence and Divergence of the ScaleInvariant (1+1)ES in Noisy Environments
LogLinear Convergence and Divergence of the ScaleInvariant (1+1)ES in Noisy Environments,10.1007/s0045301094033,Algorithmica,Mohamed Jebalia,Anne
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LogLinear Convergence and Divergence of the ScaleInvariant (1+1)ES in Noisy Environments
(
Citations: 2
)
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Mohamed Jebalia
,
Anne Auger
,
Nikolaus Hansen
Noise is present in many realworld
continuous optimization
problems.
Stochastic search
algorithms such as Evolution Strategies (ESs) have been proposed as effective search methods in such contexts. In this paper, we provide a
mathematical analysis
of the convergence of a (1+1)ES on unimodal spherical objective functions in the presence of noise. We prove for a
multiplicative noise
model that for a positive expected value of the noisy objective function, convergence or divergence happens depending on the infimum of the support of the noise. Moreover, we investigate convergence rates and show that loglinear convergence is preserved in presence of noise. This result is a strong
theoretical foundation
of the robustness of ESs with respect to noise.
Journal:
Algorithmica
, vol. 59, no. 3, pp. 425460, 2011
DOI:
10.1007/s0045301094033
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Citation Context
(2)
...cause we suspect that the results on fSchw are artificial and only reflect the fact that the model used in lmmCMA is quadratic and (2) the noisy sphere function fNSphere whose definition has been modified following the recommendations of [
6
]...
Zyed Bouzarkouna
,
et al.
Investigating the LocalMetaModel CMAES for Large Population Sizes
...where g :[ 0 , ∞[� R is a strictly increasing function, x ∈ R d and � .� denotes the Euclidean norm on R d . Loglinear behavior holds also when minimizng spherical func tions perturbed by noise [
11
]...
Mohamed Jebalia
,
et al.
LogLinear Convergence of the ScaleInvariant (µ/µw, lambda)ES and Opt...
References
(31)
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(
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Journal:
IEEE Transactions on Evolutionary Computation  TEC
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(
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Dirk V. Arnold
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Journal:
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Citations
(2)
Investigating the LocalMetaModel CMAES for Large Population Sizes
(
Citations: 1
)
Zyed Bouzarkouna
,
Anne Auger
,
Didier Yu Ding
Conference:
EvoWorkshops
, pp. 402411, 2010
LogLinear Convergence of the ScaleInvariant (µ/µw, lambda)ES and Optimal µ for Intermediate Recombination for Large Population Sizes
(
Citations: 1
)
Mohamed Jebalia
,
Anne Auger
Conference:
Parallel Problem Solving from Nature  PPSN
, pp. 5262, 2010