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Learning decompositions of expensive-to-evaluate black-box functions promisesto scale Bayesian optimisation (BO) to high-dimensional problems. However, thesuccess of these techniques depends on finding proper decompositions thataccurately represent the black-box. While previous works learn thosedecompositions based on data, we investigate data-independent decompositionsampling rules in this paper. We find that data-driven learners ofdecompositions can be easily misled towards local decompositions that do nothold globally across the search space. Then, we formally show that a randomtree-based decomposition sampler exhibits favourable theoretical guaranteesthat effectively trade off maximal information gain and functional mismatchbetween the actual black-box and its surrogate as provided by thedecomposition. Those results motivate the development of the randomdecomposition upper-confidence bound algorithm (RDUCB) that is straightforwardto implement - (almost) plug-and-play - and, surprisingly, yields significantempirical gains compared to the previous state-of-the-art on a comprehensiveset of benchmarks. We also confirm the plug-and-play nature of our modellingcomponent by integrating our method with HEBO, showing improved practical gainsin the highest dimensional tasks from Bayesmark.

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