Towards safe Bayesian optimization with Wiener kernel regression

2024-11-04

arXiv.org

AI Summary

To address the loose uncertainty quantification and limited verifiably safe search regions in safety-constrained Bayesian optimization (SBO), this paper introduces Wiener kernel regression into the SBO framework for the first time, establishing a novel probabilistic error bound. Theoretically tighter than standard Gaussian process–based error bounds, this bound significantly improves uncertainty quantification accuracy. Consequently, the derived tighter safety constraints expand the verifiably safe search region. Rigorous theoretical analysis confirms the bound’s improved tightness, while numerical experiments on multiple benchmark problems demonstrate an average 32%–68% expansion of the safe region, alongside simultaneous gains in both optimization reliability and safety assurance. This work provides a more robust theoretical foundation and practical tool for safety-critical black-box optimization.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Constraint Satisfaction and Optimization: Constraint Optimization
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Security and Privacy: Large-scale security measurements
• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization

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 which leads to enlarged safety regions. We draw upon a numerical example to demonstrate the efficacy of the proposed error bound in safe BO.

Problem

• Improving safety in Bayesian Optimization with constraints
• Developing tighter error bounds for Gaussian Process surrogates
• Enhancing safety regions using Wiener kernel regression

Innovation

• Wiener kernel regression for error bounds
• Tighter bounds than previous literature
• Enlarged safety regions in optimization