Analysis of runtime of optimization algorithms for noisy functions over discrete codomains
We consider in this work the application of optimization algorithms to problems over discrete codomains corrupted by additive unbiased noise. We propose a modification of the algorithms by repeating the fitness evaluation of the noisy function sufficiently so that, with a fix probability, the functi...
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| Vydáno v: | Theoretical computer science Ročník 605; s. 42 - 50 |
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| Jazyk: | angličtina |
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Elsevier B.V
09.11.2015
Elsevier |
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| ISSN: | 0304-3975, 1879-2294 |
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| Abstract | We consider in this work the application of optimization algorithms to problems over discrete codomains corrupted by additive unbiased noise.
We propose a modification of the algorithms by repeating the fitness evaluation of the noisy function sufficiently so that, with a fix probability, the function evaluation on the noisy case is identical to the true value.
If the runtime of the algorithms on the noise-free case is known, the number of resampling is chosen accordingly. If not, the number of resampling is chosen regarding to the number of fitness evaluations, in an anytime manner.
We conclude that if the additive noise is Gaussian, then the runtime on the noisy case, for an adapted algorithm using resamplings, is similar to the runtime on the noise-free case: we incur only an extra logarithmic factor. If the noise is non-Gaussian but with finite variance, then the total runtime of the noisy case is quadratic in function of the runtime on the noise-free case. |
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| AbstractList | We consider in this work the application of optimization algorithms to problems over discrete codomains corrupted by additive unbiased noise.
We propose a modification of the algorithms by repeating the fitness evaluation of the noisy function sufficiently so that, with a fix probability, the function evaluation on the noisy case is identical to the true value.
If the runtime of the algorithms on the noise-free case is known, the number of resampling is chosen accordingly. If not, the number of resampling is chosen regarding to the number of fitness evaluations, in an anytime manner.
We conclude that if the additive noise is Gaussian, then the runtime on the noisy case, for an adapted algorithm using resamplings, is similar to the runtime on the noise-free case: we incur only an extra logarithmic factor. If the noise is non-Gaussian but with finite variance, then the total runtime of the noisy case is quadratic in function of the runtime on the noise-free case. We consider in this work the application of optimization algorithms to problems over discrete codomains corrupted by additive unbiased noise. We propose a modification of the algorithms by repeating the fitness evaluation of the noisy function sufficiently so that, with a fix probability, the function evaluation on the noisy case is identical to the true value. If the runtime of the algorithms on the noise-free case is known, the number of resampling is chosen accordingly. If not, the number of resampling is chosen regarding to the number of fitness evaluations, in an anytime manner. We conclude that if the additive noise is Gaussian, then the runtime on the noisy case, for an adapted algorithm using resamplings, is similar to the runtime on the noise-free case: we incur only an extra logarithmic factor. If the noise is non-Gaussian but with finite variance, then the total runtime of the noisy case is quadratic in function of the runtime on the noise-free case. |
| Author | Teytaud, Olivier Akimoto, Youhei Astete-Morales, Sandra |
| Author_xml | – sequence: 1 givenname: Youhei orcidid: 0000-0003-2760-8123 surname: Akimoto fullname: Akimoto, Youhei email: y_akimoto@shinshu-u.ac.jp organization: Institute of Engineering, Shinshu University, Wakasato 4-17-1, Nagano, Japan – sequence: 2 givenname: Sandra surname: Astete-Morales fullname: Astete-Morales, Sandra email: sandra-cecilia.astete-morales@inria.fr organization: TAO (INRIA) LRI, Bat 650 Ada Lovelace, Université Paris Sud, 91405, Orsay, France – sequence: 3 givenname: Olivier surname: Teytaud fullname: Teytaud, Olivier email: olivier.teytaud@inria.fr organization: TAO (INRIA) LRI, Bat 650 Ada Lovelace, Université Paris Sud, 91405, Orsay, France |
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| Cites_doi | 10.1016/S0304-3975(01)00182-7 10.1109/TEVC.2005.859467 10.1023/B:JOGO.0000049094.73665.7e 10.1214/aoms/1177699070 10.1162/EVCO_a_00050 10.1007/s00453-010-9403-3 10.1007/s00453-010-9387-z 10.1002/aic.11579 10.1007/s00224-004-1177-z |
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| Keywords | Additive noise Runtime analysis Discrete optimization Discrete Optimization |
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| SubjectTerms | Additive noise Algorithms Discrete optimization Fitness Mathematical analysis Mathematical models Mathematics Noise Optimization Optimization and Control Resampling Run time (computers) Runtime analysis |
| Title | Analysis of runtime of optimization algorithms for noisy functions over discrete codomains |
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