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.

翻译：贝叶斯优化（BO）是一种针对昂贵黑箱优化问题的流行且样本高效的优化技术。制造业中常出现的一类问题是在随机扰动条件下最大化设计的可靠性（或等价地最小化失效概率），这类问题可能涉及极低概率的失效事件（$P_\mathrm{fail} = 10^{-6}-10^{-8}$）。本研究提出了两种基于汤普森采样与知识梯度的贝叶斯优化方法，其中知识梯度方法通过近似一步贝叶斯最优策略来最小化失效概率的对数值。两种方法均融合了重要性采样技术以应对极低失效概率场景。实验结果表明，所提方法在极端与非极端概率区间均优于现有方法。