Towards safe Bayesian optimization with Wiener kernel regression

TL;DR

This paper introduces a new, tighter error bound for Bayesian Optimization with Gaussian Process surrogates using Wiener kernel regression, enhancing safety guarantees in optimization tasks.

Contribution

The paper proposes a novel error bound based on Wiener kernel regression that improves safety region estimates in Bayesian Optimization with Gaussian processes.

Findings

The new error bound is tighter than existing bounds.

Enhanced safety regions in Bayesian Optimization.

Numerical example demonstrates improved safety performance.

Abstract

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.