We present Bayesian Binary Search (BBS), a novel probabilistic variant of the classical binary search/bisection algorithm. BBS leverages machine learning/statistical techniques to estimate the probability density of the search space and modifies the bisection step to split based on probability density rather than the traditional midpoint, allowing for the learned distribution of the search space to guide the search algorithm. Search space density estimation can flexibly be performed using supervised probabilistic machine learning techniques (e.g., Gaussian process regression, Bayesian neural networks, quantile regression) or unsupervised learning algorithms (e.g., Gaussian mixture models, kernel density estimation (KDE), maximum likelihood estimation (MLE)). We demonstrate significant efficiency gains of using BBS on both simulated data across a variety of distributions and in a real-world binary search use case of probing channel balances in the Bitcoin Lightning Network, for which we have deployed the BBS algorithm in a production setting.

翻译：我们提出贝叶斯二分搜索（BBS），这是对经典二分搜索/二分法算法的一种新颖概率化变体。BBS利用机器学习/统计技术来估计搜索空间的概率密度，并修改二分步骤，使其基于概率密度而非传统中点进行划分，从而允许利用学习到的搜索空间分布来指导搜索算法。搜索空间密度估计可以灵活地使用监督式概率机器学习技术（例如高斯过程回归、贝叶斯神经网络、分位数回归）或无监督学习算法（例如高斯混合模型、核密度估计（KDE）、最大似然估计（MLE））来执行。我们通过在多种分布上的模拟数据，以及在一个真实世界的二分搜索用例——探测比特币闪电网络中的通道余额（我们已在生产环境中部署了BBS算法）中，证明了使用BBS能带来显著的效率提升。