On Multiplicative Noise Models for Stochastic Search

  • Authors:
  • Mohamed Jebalia;Anne Auger

  • Affiliations:
  • TAO Team, INRIA Saclay, Université Paris Sud, LRI, Orsay cedex, France 91405;TAO Team, INRIA Saclay, Université Paris Sud, LRI, Orsay cedex, France 91405 and Microsoft Research-INRIA Joint Centre, Orsay Cedex, France 91893

  • Venue:
  • Proceedings of the 10th international conference on Parallel Problem Solving from Nature: PPSN X
  • Year:
  • 2008

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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.