Are Random Decompositions all we need in High Dimensional Bayesian Optimisation?

• URL: http://arxiv.org/abs/2301.12844v2
• Date: Mon, 29 May 2023 13:59:15 GMT
• Title: Are Random Decompositions all we need in High Dimensional Bayesian Optimisation?
• Authors: Juliusz Ziomek, Haitham Bou-Ammar
• Abstract summary: We find that data-driven learners of decompositions can be easily misled towards local decompositions that do not hold globally. A random tree-based decomposition sampler exhibits favourable theoretical guarantees that effectively trade off maximal information gain and functional mismatch between the actual black-box and its surrogate. Those results motivate the development of the random decomposition upper-confidence bound algorithm (RDUCB) that is straightforward to implement - (almost) plug-and-play.
• Score: 4.31133019086586
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Learning decompositions of expensive-to-evaluate black-box functions promises to scale Bayesian optimisation (BO) to high-dimensional problems. However, the success of these techniques depends on finding proper decompositions that accurately represent the black-box. While previous works learn those decompositions based on data, we investigate data-independent decomposition sampling rules in this paper. We find that data-driven learners of decompositions can be easily misled towards local decompositions that do not hold globally across the search space. Then, we formally show that a random tree-based decomposition sampler exhibits favourable theoretical guarantees that effectively trade off maximal information gain and functional mismatch between the actual black-box and its surrogate as provided by the decomposition. Those results motivate the development of the random decomposition upper-confidence bound algorithm (RDUCB) that is straightforward to implement - (almost) plug-and-play - and, surprisingly, yields significant empirical gains compared to the previous state-of-the-art on a comprehensive set of benchmarks. We also confirm the plug-and-play nature of our modelling component by integrating our method with HEBO, showing improved practical gains in the highest dimensional tasks from Bayesmark.

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