Maximizing Reliability with Bayesian Optimization

2026-02-02

AI Summary

This work addresses the challenge of reliability-based design optimization under extremely low failure probabilities (e.g., $10^{-6}$ to $10^{-8}$) commonly encountered in manufacturing and related fields. The authors propose a novel Bayesian optimization framework that integrates knowledge gradient policies with Thompson sampling, augmented by importance sampling to efficiently handle such rare events. For the first time, the knowledge gradient strategy is employed to approximate the minimization of the logarithm of the failure probability, enabling a first-order Bayes-optimal design update. Experimental results demonstrate that the proposed method substantially outperforms existing approaches in both extreme and non-extreme failure scenarios, achieving significant improvements in sample efficiency and optimization accuracy.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Sampling/Simulation-based Search
• Machine Learning: Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

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.

Problem

• reliability maximization
• rare failure probability
• black-box optimization
• manufacturing design
• extreme event

Innovation

• Bayesian optimization
• Thompson sampling
• knowledge gradient
• importance sampling
• rare event simulation