When Do Heavy-Tail Distributions Help?
N. Hansen, F. Gemperle, A. Auger, P. Koumoutsakos
Abstract. We examine the evidence for the widespread belief that
heavy tail distributions enhance the search for minima on multimodal
objective functions. We analyze isotropic and anisotropic
heavy-tail Cauchy distributions and investigate the probability to
sample a better solution, depending on the step length and the
dimensionality of the search space. The probability decreases fast
with increasing step length for isotropic Cauchy distributions and
moderate search space dimension. The anisotropic Cauchy
distribution maintains a large probability for sampling large steps
along the coordinate axes, resulting in an exceptionally good
performance on the separable multimodal Rastrigin function. In
contrast, on a non-separable rotated Rastrigin function or for the
isotropic Cauchy distribution the performance difference to a
Gaussian search distribution is negligible.
In: Ninth International Conference on Parallel Problem Solving from
Nature PPSN IX, Proceedings, pp.62-71, Berlin: Springer, 2006.