Provable Accelerated Bayesian Optimization with Knowledge Transfer

TL;DR

This paper introduces DeltaBO, a Bayesian optimization method that leverages source task knowledge to accelerate target task optimization with theoretical guarantees and empirical validation.

Contribution

DeltaBO provides a novel uncertainty-quantification approach on the difference function, enabling provable acceleration in Bayesian optimization with knowledge transfer.

Findings

DeltaBO achieves regret of order  ext{( extstyle ilde{O}( extstyle oot{2} ext{T}(T/N + extgamma_ extdelta))})} under mild assumptions.

Empirical results show DeltaBO outperforms baseline methods on real-world hyperparameter tuning and synthetic functions.

Theoretical analysis confirms the effectiveness of transfer learning in Bayesian optimization with different RKHSs.

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 $\delta$ 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 $\widetilde{O}(\sqrt{T (T/N + \gamma_\delta)})$, 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 $\gamma_\delta$ 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.