Provable Accelerated Bayesian Optimization with Knowledge Transfer

arXiv:2511.03125v2 Announce Type: replace-cross Abstract: We study how to accelerate Bayesian optimization (BO) on a target task by transferring historical knowledge from related source tasks. Existing work on BO with knowledge transfer either lacks theoretical guarantees or achieves the same regret as BO in the non-transfer setting, widetilde{O}(sqrt{T gamma_f}), where T is the number of evaluations of the target function and gamma_f denotes its information gain. In this paper, we propose the DeltaBO algorithm, which builds a novel uncertainty-quantification approach on the difference function elta between the source and target functions, which are allowed to belong to different Reproducing Kernel Hilbert Spaces (RKHSs). Under mild assumptions, we prove that the regret of DeltaBO is of order widetilde{O}(sqrt{T (T/N + gamma_elta)}), where N denotes the number of evaluations from source tasks and typically N gg T. In many applications, source and target tasks are similar, which implies that gamma_elta can be much smaller than gamma_f. Empirical studies on both real-world hyperparameter-tuning tasks and synthetic functions show that DeltaBO outperforms other baseline methods and also verify our theoretical claims. Our code is available on GitHub.

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Source: arXiv cs.LG | 2026-04-29