Log-Linear Convergence and Divergence of the Scale-Invariant (1+1)-ES in Noisy Environments

@article{Jebalia2010LogLinearCA,
  title={Log-Linear Convergence and Divergence of the Scale-Invariant (1+1)-ES in Noisy Environments},
  author={Mohamed Jebalia and Anne Auger and Nikolaus Hansen},
  journal={Algorithmica},
  year={2010},
  volume={59},
  pages={425-460}
}
Noise is present in many real-world 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… CONTINUE READING