Towards safe Bayesian optimization with Wiener kernel regression
This work addresses safety constraints in Bayesian optimization, which is crucial for applications like robotics and autonomous systems, but it is incremental as it builds on prior error bound methods.
The paper tackles the problem of ensuring safety in Bayesian optimization by developing a novel error bound for Gaussian Process surrogates using Wiener kernel regression, which is proven to be tighter than existing bounds and leads to enlarged safety regions.
Bayesian Optimization (BO) is a data-driven strategy for minimizing/maximizing black-box functions based on probabilistic surrogate models. In the presence of safety constraints, the performance of BO crucially relies on tight probabilistic error bounds related to the uncertainty surrounding the surrogate model. For the case of Gaussian Process surrogates and Gaussian measurement noise, we present a novel error bound based on the recently proposed Wiener kernel regression. We prove that under rather mild assumptions, the proposed error bound is tighter than bounds previously documented in the literature, leading to enlarged safety regions. We draw upon a numerical example to demonstrate the efficacy of the proposed error bound in safe BO.