A Framework for Bayesian Optimization in Embedded Subspaces
Amin Nayebi · Alexander Munteanu · Matthias Poloczek

Tue Jun 11th 06:30 -- 09:00 PM @ Pacific Ballroom #236

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.

Author Information

Amin Nayebi (University of Arizona)
Alexander Munteanu (TU Dortmund)
Matthias Poloczek (Uber AI Labs & The University of Arizona)

**Matthias Poloczek** is an assistant professor in the Department of Systems and Industrial Engineering at the **University of Arizona**. He works in **machine learning and optimization**, with a focus on **Bayesian optimization** of expensive functions and its applications in aerospace engineering, biochemistry, and materials science. Matthias was a postdoctoral researcher with *David P. Williamson* and *Peter I. Frazier* at **Cornell University** , after he obtained his Ph.D. from the **Goethe-University** Frankfurt in 2013, advised by *Georg Schnitger*.

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