Ong, Yean Hoon; (2025) Bayesian Optimisation Using Product of Local Gaussian Process Models. Doctoral thesis (Ph.D), UCL (University College London).

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Abstract

Bayesian optimisation (BO) is a powerful strategy for optimising black-box functions that involve expensive evaluations. In BO, the effective modelling of black-box functions using the Gaussian process (GP) model remains a challenge. The commonly used GP model is a single global GP (GP-glo) or a collection of independent local GPs (GP-ind). In comparison to the GP-glo and GP-ind models, the product of local GP models (GP-pro), which consists of a collection of collaborative local GPs, has the advantage of alleviating the issue of cubic computational cost while being capable of capturing the local patterns and global correlations. However, the current approaches of using GP-pro models in BO yield less satisfactory performance than BO algorithms using GP-glo and GP-ind models. The aim of this thesis is to study approaches to enhance the use of GP-pro models in terms of performance and computational overhead in BO settings. This thesis makes three contributions. First, this thesis proposes an information-based method for calibrating the overestimated variances encountered in the GP-pro model. Second, this thesis presents comprehensive comparative studies to demonstrate the advantages of using the GP-pro model with uncertainty calibration (GP-pro-c) in BO settings involving various acquisition functions. Third, this thesis introduces an effective approach for coupling the GP-pro-c model with the trust region method for large-scale and high-dimensional BO. Overall, the experimental results presented in this thesis strongly favour the GP-pro-c model, which achieved 2.3% and 12.0% lower NLL and ENCE scores than GP-pro with no calibration. In the BO settings, the BO algorithm using the GP-pro-c model achieved 0.9% and 39.4% lower simple regret and computational overhead, respectively, than the BO algorithm using the GP-glo model. Additionally, the BO algorithm using the GP-pro-c model with trust regions reduced the simple regret and computational overhead by 2.6% and 34.9%, respectively, compared with the BO algorithm using the GP-ind model with trust regions.

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