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Bayesian Optimization over High-Dimensional Combinatorial Spaces via Dictionary-based Embeddings

3 Mar 2023arXiv:2303.01774archive 2025-07-28

Aryan Deshwal, Sebastian Ament, Maximilian Balandat, Eytan Bakshy, Janardhan Rao Doppa, David Eriksson

We consider the problem of optimizing expensive black-box functions over high-dimensional combinatorial spaces which arises in many science, engineering, and ML applications. We use Bayesian Optimization (BO) and propose a novel surrogate modeling approach for efficiently handling a large number of binary and categorical parameters. The key idea is to select a number of discrete structures from the input space (the dictionary) and use them to define an ordinal embedding for high-dimensional combinatorial structures. This allows us to use existing Gaussian process models for continuous spaces. We develop a principled approach based on binary wavelets to construct dictionaries for binary spaces, and propose a randomized construction method that generalizes to categorical spaces. We provide theoretical justification to support the effectiveness of the dictionary-based embeddings. Our experiments on diverse real-world benchmarks demonstrate the effectiveness of our proposed surrogate modeling approach over state-of-the-art BO methods.

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