On Multiplicative Noise Models for Stochastic Search

  • Mohamed Jebalia
  • Anne Auger
Conference paper

DOI: 10.1007/978-3-540-87700-4_6

Part of the Lecture Notes in Computer Science book series (LNCS, volume 5199)
Cite this paper as:
Jebalia M., Auger A. (2008) On Multiplicative Noise Models for Stochastic Search. In: Rudolph G., Jansen T., Beume N., Lucas S., Poloni C. (eds) Parallel Problem Solving from Nature – PPSN X. PPSN 2008. Lecture Notes in Computer Science, vol 5199. Springer, Berlin, Heidelberg

Abstract

In this paper we investigate multiplicative noise models in the context of continuous optimization. We illustrate how some intrinsic properties of the noise model imply the failure of reasonable search algorithms for locating the optimum of the noiseless part of the objective function. Those findings are rigorously investigated on the (1 + 1)-ES for the minimization of the noisy sphere function. Assuming a lower bound on the support of the noise distribution, we prove that the (1 + 1)-ES diverges when the lower bound allows to sample negative fitness with positive probability and converges in the opposite case. We provide a discussion on the practical applications and non applications of those outcomes and explain the differences with previous results obtained in the limit of infinite search-space dimensionality.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Mohamed Jebalia
    • 1
  • Anne Auger
    • 1
    • 2
  1. 1.TAO Team, INRIA SaclayUniversité Paris Sud, LRIOrsay cedexFrance
  2. 2.Microsoft Research-INRIA Joint CentreOrsay CedexFrance

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