# Maximizing Reliability with Bayesian Optimization

arXiv: https://arxiv.org/abs/2602.02432 · HTML: https://mlsanity.com/paper/2602.02432/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 52 references that are in the map.
- First posted on arXiv 2 Feb 2026.

## Builds on (most cited first, 17 of 17)

- [Efficiently Sampling Functions from Gaussian Process Posteriors](https://mlsanity.com/paper/2002.09309/) (2020)
- [Pathwise Conditioning of Gaussian Processes](https://mlsanity.com/paper/2011.04026/) (2020)
- [Robust Multi-Objective Bayesian Optimization Under Input Noise](https://mlsanity.com/paper/2202.07549/) (2022)
- [Bayesian Optimization of Risk Measures](https://mlsanity.com/paper/2007.05554/) (2020)
- [Value-at-Risk Optimization with Gaussian Processes](https://mlsanity.com/paper/2105.06126/) (2021)
- [Bayesian Quantile and Expectile Optimisation](https://mlsanity.com/paper/2001.04833/) (2020)
- [Bayesian Optimization of Function Networks with Partial Evaluations](https://mlsanity.com/paper/2311.02146/) (2023)
- [Exploring Exploration in Bayesian Optimization](https://mlsanity.com/paper/2502.08208/) (2025)
- [A Robust Multi-Objective Bayesian Optimization Framework Considering Input Uncertainty](https://mlsanity.com/paper/2202.12848/) (2022)
- [Knowledge Gradient for Multi-Objective Bayesian Optimization with Decoupled Evaluations](https://mlsanity.com/paper/2302.01310/) (2023)
- [Hamiltonian MCMC methods for estimating rare events probabilities in high-dimensional problems](https://mlsanity.com/paper/2007.00180/) (2020)
- [Large deviation theory-based adaptive importance sampling for rare events in high dimensions](https://mlsanity.com/paper/2209.06278/) (2022)
- [Maximizing the Success Probability of Policy Allocations in Online Systems](https://mlsanity.com/paper/2312.16267/) (2023)
- [A sampling criterion for constrained Bayesian optimization with uncertainties](https://mlsanity.com/paper/2103.05706/) (2021)
- [Two-stage Design for Failure Probability Estimation with Gaussian Process Surrogates](https://mlsanity.com/paper/2410.04496/) (2024)
- [Coupling and selecting constraints in Bayesian optimization under uncertainties](https://mlsanity.com/paper/2204.00527/) (2022)
- [Bayesian Optimization for Non-Convex Two-Stage Stochastic Optimization Problems](https://mlsanity.com/paper/2408.17387/) (2024)

## Abstract (arXiv)

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 (Pfail = 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.