A Robust Asymmetric Kernel Function for Bayesian Optimization, with Application to Image Defect Detection in Manufacturing Systems

TL;DR

This paper introduces a new robust asymmetric kernel function, AEN-RBF, for Bayesian optimization, which improves robustness to outliers and accelerates convergence, demonstrated through applications in image defect detection in manufacturing.

Contribution

The paper proposes the AEN-RBF kernel, a novel asymmetric kernel function that enhances robustness and convergence speed in Bayesian optimization, especially in outlier-prone scenarios.

Findings

AEN-RBF reduces mean squared prediction error compared to RBF.

AEN-RBF achieves faster convergence to the global optimum.

AEN-RBF outperforms benchmark kernels in synthetic and real-world tests.

Abstract

Some response surface functions in complex engineering systems are usually highly nonlinear, unformed, and expensive-to-evaluate. To tackle this challenge, Bayesian optimization, which conducts sequential design via a posterior distribution over the objective function, is a critical method used to find the global optimum of black-box functions. Kernel functions play an important role in shaping the posterior distribution of the estimated function. The widely used kernel function, e.g., radial basis function (RBF), is very vulnerable and susceptible to outliers; the existence of outliers is causing its Gaussian process surrogate model to be sporadic. In this paper, we propose a robust kernel function, Asymmetric Elastic Net Radial Basis Function (AEN-RBF). Its validity as a kernel function and computational complexity are evaluated. When compared to the baseline RBF kernel, we prove theoretically that AEN-RBF can realize smaller mean squared prediction error under mild conditions. The proposed AEN-RBF kernel function can also realize faster convergence to the global optimum. We also show that the AEN-RBF kernel function is less sensitive to outliers, and hence improves the robustness of the corresponding Bayesian optimization with Gaussian processes. Through extensive evaluations carried out on synthetic and real-world optimization problems, we show that AEN-RBF outperforms existing benchmark kernel functions.