Abstract
This works extends the Random Embedding Bayesian Optimization approach by integrating a warping of the high dimensional subspace within the covariance kernel. The proposed warping, that relies on elementary geometric considerations, allows mitigating the drawbacks of the high extrinsic dimensionality while avoiding the algorithm to evaluate points giving redundant information. It also alleviates constraints on bound selection for the embedded domain, thus improving the robustness, as illustrated with a test case with 25 variables and intrinsic dimension 6.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Jones, D., Schonlau, M., Welch, W.: Efficient global optimization of expensive black-box functions. J. Global Optim. 13(4), 455–492 (1998)
Koziel, S., Ciaurri, D.E., Leifsson, L.: Surrogate-based methods. In: Koziel, S., Yang, X.-S. (eds.) Comput. Optimization, Methods and Algorithms. SCI, vol. 356, pp. 33–59. Springer, Heidelberg (2011)
Matheron, G.: Principles of geostatistics. Econ. Geol. 58(8), 1246–1266 (1963)
Mockus, J., Tiesis, V., Zilinskas, A.: The application of Bayesian methods for seeking the extremum. In: Dixon, L., Szego, G. (eds.) Towards Global Optimization, vol. 2, pp. 117–129. Elsevier, Amsterdam (1978)
Rasmussen, C.E., Williams, C.: Gaussian Processes for Machine Learning. MIT Press, Cambridge (2006). http://www.gaussianprocess.org/gpml/
Roustant, O., Ginsbourger, D., Deville, Y.: DiceKriging, DiceOptim: two R packages for the analysis of computer experiments by kriging-based metamodeling and optimization. J. Stat. Softw. 51(1), 1–55 (2012)
Snoek, J., Swersky, K., Zemel, R.S., Adams, R.P.: Input warping for Bayesian optimization of non-stationary functions. In ICML (2014)
Stein, M.L.: Interpolation of Spatial Data: Some Theory for Kriging. Springer, New York (1999)
Wang, Z., Zoghi, M., Hutter, F., Matheson, D., de Freitas, N.: Bayesian optimization in high dimensions via random embeddings. In: IJCAI (2013)
Acknowledgments
This work has been conducted within the frame of the ReDice Consortium, gathering industrial (CEA, EDF, IFPEN, IRSN, Renault) and academic (Ecole des Mines de Saint-Etienne, INRIA, and the University of Bern) partners around advanced methods for Computer Experiments.
The authors also thanks the anonymous reviewers as well as Frank Hutter for their helpful suggestions.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this paper
Cite this paper
Binois, M., Ginsbourger, D., Roustant, O. (2015). A Warped Kernel Improving Robustness in Bayesian Optimization Via Random Embeddings. In: Dhaenens, C., Jourdan, L., Marmion, ME. (eds) Learning and Intelligent Optimization. LION 2015. Lecture Notes in Computer Science(), vol 8994. Springer, Cham. https://doi.org/10.1007/978-3-319-19084-6_28
Download citation
DOI: https://doi.org/10.1007/978-3-319-19084-6_28
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-19083-9
Online ISBN: 978-3-319-19084-6
eBook Packages: Computer ScienceComputer Science (R0)