Maximizing Reliability with Bayesian Optimization

TL;DR

This paper introduces two Bayesian optimization methods using Thompson sampling and knowledge gradient, enhanced with importance sampling, to efficiently maximize reliability and minimize failure probability in manufacturing designs, especially for extremely rare failures.

Contribution

The paper develops novel BO algorithms that incorporate importance sampling to effectively handle very rare failure probabilities, outperforming existing methods.

Findings

Proposed methods outperform existing approaches in extreme failure regimes.

Incorporating importance sampling improves efficiency in rare event optimization.

Methods are effective for minimizing failure probabilities as low as 10^{-8}.

Abstract

Bayesian optimization (BO) is a popular, sample-efficient technique for expensive, black-box optimization. One such problem arising in manufacturing is that of maximizing the reliability, or equivalently minimizing the probability of a failure, of a design which is subject to random perturbations - a problem that can involve extremely rare failures ($P_\mathrm{fail} = 10^{-6}-10^{-8}$). In this work, we propose two BO methods based on Thompson sampling and knowledge gradient, the latter approximating the one-step Bayes-optimal policy for minimizing the logarithm of the failure probability. Both methods incorporate importance sampling to target extremely small failure probabilities. Empirical results show the proposed methods outperform existing methods in both extreme and non-extreme regimes.