Bayesian Optimization over Hybrid Spaces

Aryan Deshwal, Syrine Belakaria, Janardhan Rao Doppa
Proceedings of the 38th International Conference on Machine Learning, PMLR 139:2632-2643, 2021.

Abstract

We consider the problem of optimizing hybrid structures (mixture of discrete and continuous input variables) via expensive black-box function evaluations. This problem arises in many real-world applications. For example, in materials design optimization via lab experiments, discrete and continuous variables correspond to the presence/absence of primitive elements and their relative concentrations respectively. The key challenge is to accurately model the complex interactions between discrete and continuous variables. In this paper, we propose a novel approach referred as Hybrid Bayesian Optimization (HyBO) by utilizing diffusion kernels, which are naturally defined over continuous and discrete variables. We develop a principled approach for constructing diffusion kernels over hybrid spaces by utilizing the additive kernel formulation, which allows additive interactions of all orders in a tractable manner. We theoretically analyze the modeling strength of additive hybrid kernels and prove that it has the universal approximation property. Our experiments on synthetic and six diverse real-world benchmarks show that HyBO significantly outperforms the state-of-the-art methods.

Cite this Paper

BibTeX
@InProceedings{pmlr-v139-deshwal21a, title = {Bayesian Optimization over Hybrid Spaces}, author = {Deshwal, Aryan and Belakaria, Syrine and Doppa, Janardhan Rao}, booktitle = {Proceedings of the 38th International Conference on Machine Learning}, pages = {2632--2643}, year = {2021}, editor = {Meila, Marina and Zhang, Tong}, volume = {139}, series = {Proceedings of Machine Learning Research}, month = {18--24 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v139/deshwal21a/deshwal21a.pdf}, url = {https://proceedings.mlr.press/v139/deshwal21a.html}, abstract = {We consider the problem of optimizing hybrid structures (mixture of discrete and continuous input variables) via expensive black-box function evaluations. This problem arises in many real-world applications. For example, in materials design optimization via lab experiments, discrete and continuous variables correspond to the presence/absence of primitive elements and their relative concentrations respectively. The key challenge is to accurately model the complex interactions between discrete and continuous variables. In this paper, we propose a novel approach referred as Hybrid Bayesian Optimization (HyBO) by utilizing diffusion kernels, which are naturally defined over continuous and discrete variables. We develop a principled approach for constructing diffusion kernels over hybrid spaces by utilizing the additive kernel formulation, which allows additive interactions of all orders in a tractable manner. We theoretically analyze the modeling strength of additive hybrid kernels and prove that it has the universal approximation property. Our experiments on synthetic and six diverse real-world benchmarks show that HyBO significantly outperforms the state-of-the-art methods.} }
Endnote
%0 Conference Paper %T Bayesian Optimization over Hybrid Spaces %A Aryan Deshwal %A Syrine Belakaria %A Janardhan Rao Doppa %B Proceedings of the 38th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2021 %E Marina Meila %E Tong Zhang %F pmlr-v139-deshwal21a %I PMLR %P 2632--2643 %U https://proceedings.mlr.press/v139/deshwal21a.html %V 139 %X We consider the problem of optimizing hybrid structures (mixture of discrete and continuous input variables) via expensive black-box function evaluations. This problem arises in many real-world applications. For example, in materials design optimization via lab experiments, discrete and continuous variables correspond to the presence/absence of primitive elements and their relative concentrations respectively. The key challenge is to accurately model the complex interactions between discrete and continuous variables. In this paper, we propose a novel approach referred as Hybrid Bayesian Optimization (HyBO) by utilizing diffusion kernels, which are naturally defined over continuous and discrete variables. We develop a principled approach for constructing diffusion kernels over hybrid spaces by utilizing the additive kernel formulation, which allows additive interactions of all orders in a tractable manner. We theoretically analyze the modeling strength of additive hybrid kernels and prove that it has the universal approximation property. Our experiments on synthetic and six diverse real-world benchmarks show that HyBO significantly outperforms the state-of-the-art methods.
APA
Deshwal, A., Belakaria, S. & Doppa, J.R.. (2021). Bayesian Optimization over Hybrid Spaces. Proceedings of the 38th International Conference on Machine Learning, in Proceedings of Machine Learning Research 139:2632-2643 Available from https://proceedings.mlr.press/v139/deshwal21a.html.

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