Active learning optimizes the exploration of large parameter spaces by
strategically selecting which experiments or simulations to conduct, thus
reducing resource consumption and potentially accelerating scientific
discovery. A key component of this approach is a probabilistic surrogate model,
typically a Gaussian Process (GP), which approximates an unknown functional
relationship between control parameters and a target property. However,
conventional GPs often struggle when applied to systems with discontinuities
and non-stationarities, prompting the exploration of alternative models. This
limitation becomes particularly relevant in physical science problems, which
are often characterized by abrupt transitions between different system states
and rapid changes in physical property behavior. Fully Bayesian Neural Networks
(FBNNs) serve as a promising substitute, treating all neural network weights
probabilistically and leveraging advanced Markov Chain Monte Carlo techniques
for direct sampling from the posterior distribution. This approach enables
FBNNs to provide reliable predictive distributions, crucial for making informed
decisions under uncertainty in the active learning setting. Although
traditionally considered too computationally expensive for 'big data'
applications, many physical sciences problems involve small amounts of data in
relatively low-dimensional parameter spaces. Here, we assess the suitability
and performance of FBNNs with the No-U-Turn Sampler for active learning tasks
in the 'small data' regime, highlighting their potential to enhance predictive
accuracy and reliability on test functions relevant to problems in physical
sciences.

主题：主动学习、概率替代模型、高斯过程、不连续性、完全贝叶斯神经网络；摘要：评估了完全贝叶斯神经网络在小数据条件下使用无 U-Turn 采样器进行主动学习任务的适用性和性能，突显了其增加物理科学问题相关测试函数的预测准确性和可靠性的潜力。

基于完全贝叶斯神经网络的不连续和非稳态数据的主动学习

Active Learning with Fully Bayesian Neural Networks for Discontinuous  and Nonstationary Data

Accurately estimating the probability of failure for safety-critical systems
is important for certification. Estimation is often challenging due to
high-dimensional input spaces, dangerous test scenarios, and computationally
expensive simulators; thus, efficient estimation techniques are important to
study. This work reframes the problem of black-box safety validation as a
Bayesian optimization problem and introduces an algorithm, Bayesian safety
validation, that iteratively fits a probabilistic surrogate model to
efficiently predict failures. The algorithm is designed to search for failures,
compute the most-likely failure, and estimate the failure probability over an
operating domain using importance sampling. We introduce a set of three
acquisition functions that focus on reducing uncertainty by covering the design
space, optimizing the analytically derived failure boundaries, and sampling the
predicted failure regions. Mainly concerned with systems that only output a
binary indication of failure, we show that our method also works well in cases
where more output information is available. Results show that Bayesian safety
validation achieves a better estimate of the probability of failure using
orders of magnitude fewer samples and performs well across various safety
validation metrics. We demonstrate the algorithm on three test problems with
access to ground truth and on a real-world safety-critical subsystem common in
autonomous flight: a neural network-based runway detection system. This work is
open sourced and currently being used to supplement the FAA certification
process of the machine learning components for an autonomous cargo aircraft.

本文提出了一种基于贝叶斯优化的安全验证算法，它通过迭代地适配概率代理模型来高效预测故障，并通过重要性采样来估计操作域内的故障概率。经实验表明，该算法在减少样本数和各种安全验证指标方面表现良好，并可用于补充机器学习组件的 FAA 认证过程。

黑盒系统的贝叶斯安全验证

Bayesian Safety Validation for Black-Box Systems

Optimizing expensive-to-evaluate black-box functions of discrete (and
potentially continuous) design parameters is a ubiquitous problem in scientific
and engineering applications. Bayesian optimization (BO) is a popular,
sample-efficient method that leverages a probabilistic surrogate model and an
acquisition function (AF) to select promising designs to evaluate. However,
maximizing the AF over mixed or high-cardinality discrete search spaces is
challenging standard gradient-based methods cannot be used directly or
evaluating the AF at every point in the search space would be computationally
prohibitive. To address this issue, we propose using probabilistic
reparameterization (PR). Instead of directly optimizing the AF over the search
space containing discrete parameters, we instead maximize the expectation of
the AF over a probability distribution defined by continuous parameters. We
prove that under suitable reparameterizations, the BO policy that maximizes the
probabilistic objective is the same as that which maximizes the AF, and
therefore, PR enjoys the same regret bounds as the original BO policy using the
underlying AF. Moreover, our approach provably converges to a stationary point
of the probabilistic objective under gradient ascent using scalable, unbiased
estimators of both the probabilistic objective and its gradient. Therefore, as
the number of starting points and gradient steps increase, our approach will
recover of a maximizer of the AF (an often-neglected requisite for commonly
used BO regret bounds). We validate our approach empirically and demonstrate
state-of-the-art optimization performance on a wide range of real-world
applications. PR is complementary to (and benefits) recent work and naturally
generalizes to settings with multiple objectives and black-box constraints.

利用概率重参数化方法（PR）在混合或高基数离散搜索空间中最大化收购功能（AF），可显著提高贝叶斯优化（BO）的优化表现，并且能够很自然地扩展到具有多个目标和黑盒约束的设置。