Examples of inconsistency in optimization by expected improvement
Optimization and Control
2012-12-18 v2 Probability
Abstract
We consider the 1D Expected Improvement optimization based on Gaussian processes having spectral densities converging to zero faster than exponentially. We give examples of problems where the optimization trajectory is not dense in the design space. In particular, we prove that for Gaussian kernels there exist smooth objective functions for which the optimization does not converge on the optimum.
Cite
@article{arxiv.1109.1320,
title = {Examples of inconsistency in optimization by expected improvement},
author = {Dmitry Yarotsky},
journal= {arXiv preprint arXiv:1109.1320},
year = {2012}
}
Comments
Submitted to Journal of Global Optimization. Section 3 with a numerical example added; some remarks in the introduction and details of proofs added following feedback from the referees