Abstract
This paper proposes a new formulation of Gaussian process for constraints with piece-wise smooth conditions. Combining ideas from decision trees and Gaussian processes, it is shown that the new model can effectively identify the non-smooth regions and tackle the non-smoothness in piece-wise smooth constraint functions. A constrained Bayesian optimizer is then constructed to handle optimization problems with both noisy objective and constraint functions.
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References
Shahriari, B., Swersky, K., Wang, Z., Adams, R.P., Freitas, N.D.: Taking the human out of the loop: a review of Bayesian optimization. Proc. IEEE 104, 148–175 (2016)
Gardner, J.R., Kusner, M.J., Xu, Z., Weinberger, K.Q., Cunningham, J.P.: Bayesian optimization with inequality constraints. In: 31st International Conference on Machine Learning, Beijing, China, pp. 937–945 (2014)
Rasmussen, C.E., Williams, C.: Gaussian Processes for Machine Learning. The MIT Press, Cambridge (2006)
Hernandez-Lobato, J., Gelbart, M., Adams, R., Hoffman, M., Ghahramani, Z.: A general framework for constrained Bayesian optimization using information-based search. J. Mach. Learn. Res. 17, 1–53 (2016)
Letham, B., Karrer, B., Ottoni, G., Bakshy, E.: Constrained Bayesian optimization with noisy experiments (2017). https://arxiv.org/abs/1706.07094
Zlupko, T.: Portfolio optimization with discontinuous constraint. In: SAS Global Forum 2016, Las-Vegas, USA (2016)
Calandra, R., Peters, J., Rasmussen, C., Deisenroth, M.: Manifold Gaussian processes for regression (2014). http://arxiv.org/abs/1402.5876
Snoek, J., Swersky, K., Zemel, R., Adams, R.: Input warping for Bayesian optimization of non-stationary functions. In: International Conference on Machine Learning, Beijing, China, pp. 1674–1682 (2014)
Heinonen, M., Mannerstrom, H., Rousu, J., Kaski, S., Lahdesmaki, H.: Non-stationary Gaussian process regression with Hamiltonian Monte Carlo. In: 19th International Conference on Artificial Intelligence and Statistics, Cadiz, Spain, pp. 732–740 (2016)
Gramacy, R., Lee, H.: Bayesian treed Gaussian process models with an application to computer modeling. J. Am. Stat. Assoc. 103, 1119–1130 (2007)
Broderick, T., Gramacy, R.: Classification and categorical inputs with treed Gaussian process models. J. Classif. 28, 244–270 (2011)
Duvenaud, D., Lioyd, J., Grosse, R., Tenenbaum, J., Ghahramani, Z.: Structure discovery in nonparametric regression through compositional kernel search. In: 30th International Conference on Machine Learning, Atlanta, USA, pp. 1166–1174 (2013)
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Gorji Daronkolaei, A., Hajian, A., Custis, T. (2018). Constrained Bayesian Optimization for Problems with Piece-wise Smooth Constraints. In: Bagheri, E., Cheung, J. (eds) Advances in Artificial Intelligence. Canadian AI 2018. Lecture Notes in Computer Science(), vol 10832. Springer, Cham. https://doi.org/10.1007/978-3-319-89656-4_18
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DOI: https://doi.org/10.1007/978-3-319-89656-4_18
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