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Original scientific paper
https://doi.org/10.17535/crorr.2018.0001

An analysis of covariance parameters in Gaussian process-based optimization

Hossein Mohammadi ; College of Engineering, Mathematics and Physical Sciences, University of Exeter, Exeter, UK
Rodolphe Le Riche ; Mines School of Saint Etienne, H. Fayol Institute, Saint-Etienne, France
Xavier Bay ; Mines Scfool of Saint Etienne, H. Fayol Institute, Saint-Etienne, France
Eric Touboul ; Mines Scfool of Saint Etienne, H. Fayol Institute, Saint-Etienne, France

Fulltext: english, pdf (1 MB) pages 1-10 downloads: 131* cite
APA 6th Edition
Mohammadi, H., Le Riche, R., Bay, X. & Touboul, E. (2018). An analysis of covariance parameters in Gaussian process-based optimization. Croatian Operational Research Review, 9 (1), 1-10. https://doi.org/10.17535/crorr.2018.0001
MLA 8th Edition
Mohammadi, Hossein, et al. "An analysis of covariance parameters in Gaussian process-based optimization." Croatian Operational Research Review, vol. 9, no. 1, 2018, pp. 1-10. https://doi.org/10.17535/crorr.2018.0001. Accessed 22 Nov. 2019.
Chicago 17th Edition
Mohammadi, Hossein, Rodolphe Le Riche, Xavier Bay and Eric Touboul. "An analysis of covariance parameters in Gaussian process-based optimization." Croatian Operational Research Review 9, no. 1 (2018): 1-10. https://doi.org/10.17535/crorr.2018.0001
Harvard
Mohammadi, H., et al. (2018). 'An analysis of covariance parameters in Gaussian process-based optimization', Croatian Operational Research Review, 9(1), pp. 1-10. https://doi.org/10.17535/crorr.2018.0001
Vancouver
Mohammadi H, Le Riche R, Bay X, Touboul E. An analysis of covariance parameters in Gaussian process-based optimization. Croatian Operational Research Review [Internet]. 2018 [cited 2019 November 22];9(1):1-10. https://doi.org/10.17535/crorr.2018.0001
IEEE
H. Mohammadi, R. Le Riche, X. Bay and E. Touboul, "An analysis of covariance parameters in Gaussian process-based optimization", Croatian Operational Research Review, vol.9, no. 1, pp. 1-10, 2018. [Online]. https://doi.org/10.17535/crorr.2018.0001

Abstracts
The need for globally optimizing expensive-to-evaluate functions frequently occurs in many real-world applications. Among the methods developed for solving such problems, the Efficient Global Optimization (EGO) is regarded as one of the state-of-the-art unconstrained continuous optimization algorithms. The surrogate model used in EGO is a Gaussian process (GP) conditional on data points. The most important control on the efficiency of the EGO algorithm is the GP covariance function (or kernel), which is taken as a parameterized function. In this paper, we theoretically and empirically analyze the effect of the covariance parameters, the so-called "characteristic length scale" and "nugget", on EGO performance. More precisely, we analyze the EGO algorithm with fixed covariance parameters and compare them to the standard setting where they are statistically estimated. The limit behavior of EGO with very small or very large characteristic length scales is identified. Experiments show that a "small" nugget should be preferred to its maximum likelihood estimate. Overall, this study contributes to a better theoretical and practical understanding of a key optimization algorithm.

Keywords
Covariance kernel; EGO; Gaussian process; global optimization

Hrčak ID: 203889

URI
https://hrcak.srce.hr/203889

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