A lower bound on convergence rates of nonadaptive algorithms for univariate optimization with noise

Authors:
James M. Calvin
Affiliations:
Department of Computer Science, New Jersey Institute of Technology, Newark, USA 07102-1982
Venue:
Journal of Global Optimization
Year:
2010

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Abstract

This paper considers complexity bounds for the problem of approximating the global minimum of a univariate function when the function evaluations are corrupted by random noise. We take an average-case point of view, where the objective function is taken to be a sample function of a Wiener process and the noise is independent Gaussian. Previous papers have bounded the convergence rates of some nonadaptive algorithms. We establish a lower bound on the convergence rate of any nonadaptive algorithm.