On Safety in Safe Bayesian Optimization

Christian Fiedler, Johanna Menn, Lukas Kreisköther, Sebastian Trimpe

Abstract:

Safe Bayesian Optimization (BO) is increasingly used to optimize an unknown function under safety constraints, a central task in robotics, biomedical engineering, and many other disciplines. Due to the safety-critical nature of these applications, it is crucial that theoretical safety guarantees for these algorithms translate into the real world. In this work, we investigate three safety-related issues in SafeOpt-type algorithms, a popular class of safe BO methods. First, these algorithms critically rely on frequentist uncertainty bounds for Gaussian Process (GP) regression, but concrete implementations typically utilize heuristics that invalidate all safety guarantees. We provide a detailed analysis of this problem and introduce Real-$\beta$-SafeOpt, a variant of the SafeOpt algorithm that leverages recent GP bounds and thus retains all theoretical guarantees. Second, we identify a key technical assumption in SafeOpt-like algorithms, the availability of an upper bound on the reproducing kernel Hilbert space (RKHS) norm of the target function, as a central obstacle to real-world usage.
To address this issue, we propose to rely instead on a known Lipschitz and noise bound, and we introduce Lipschitz-only Safe Bayesian Optimization (LoSBO), a SafeOpt-type algorithm using the latter two assumptions. We show empirically that this algorithm is not only safe, but also outperforms the state-of-the-art on several function classes. Third, SafeOpt and derived algorithms rely on a %gridding of the search space, discrete search space, complicating their application to higher-dimensional problems. To broaden the applicability of these algorithms, we introduce Lipschitz-only Safe GP-UCB (LoS-GP-UCB), a LoSBO variant that is applicable to moderately high-dimensional problems, while retaining safety. By analyzing practical safety issues in an important class of safe BO algorithms, and providing ready-to-use algorithms that overcome these issues, this work contributes to bringing safe and reliable machine learning techniques closer to real world applications.

Submission Length: Long submission (more than 12 pages of main content)

Changes Since Last Submission: inserted OpenReview link

Code: https://github.com/Data-Science-in-Mechanical-Engineering/LoSBO

Assigned Action Editor: ~Trevor_Campbell1

Submission Number: 2711