A Framework for Bayesian Optimization in Embedded Subspaces

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Amin Nayebi, Alexander Munteanu, Matthias Poloczek ;
Proceedings of the 36th International Conference on Machine Learning, PMLR 97:4752-4761, 2019.

Abstract

We present a theoretically founded approach for high-dimensional Bayesian optimization based on low-dimensional subspace embeddings. We prove that the error in the Gaussian process model is bounded tightly when going from the original high-dimensional search domain to the low-dimensional embedding. This implies that the optimization process in the low-dimensional embedding proceeds essentially as if it were run directly on an unknown active subspace of low dimensionality. The argument applies to a large class of algorithms and GP models, including non-stationary kernels. Moreover, we provide an efficient implementation based on hashing and demonstrate empirically that this subspace embedding achieves considerably better results than the previously proposed methods for high-dimensional BO based on Gaussian matrix projections and structure-learning.

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