论文标题
双向贝叶斯优化的高量变量改善的概率分布
Probability Distribution of Hypervolume Improvement in Bi-objective Bayesian Optimization
论文作者
论文摘要
超量卷的改进（HVI）通常用于多目标贝叶斯优化算法中，以定义其占掌to的属性，以定义采集功能。这项工作不是关注HVI的特定统计矩，而是旨在为双向目标问题提供HVI概率分布的确切表达。考虑到高斯工艺（GP）建模产生的双变量高斯随机变量，我们通过基于细胞分区的方法得出其超量改进的概率分布。与HVI分布的蒙特卡洛近似相比，我们的精确表达在数值准确性和计算效率方面表现出色。利用此分布，我们提出了一种新颖的采集功能-YPREPSILON $ - 超量改进的概率（$ \ VAREPSILON $ -POHVI）。在实验上，我们表明，在许多广泛应用的双目标测试问题上，$ \ varepsilon $ -POHVI显着超过其他相关的采集功能，例如$ \ varepsilon $ -POI，并且预期的超量改进，当GP模型表现出预测不确定时，
Hypervolume improvement (HVI) is commonly employed in multi-objective Bayesian optimization algorithms to define acquisition functions due to its Pareto-compliant property. Rather than focusing on specific statistical moments of HVI, this work aims to provide the exact expression of HVI's probability distribution for bi-objective problems. Considering a bi-variate Gaussian random variable resulting from Gaussian process (GP) modeling, we derive the probability distribution of its hypervolume improvement via a cell partition-based method. Our exact expression is superior in numerical accuracy and computation efficiency compared to the Monte Carlo approximation of HVI's distribution. Utilizing this distribution, we propose a novel acquisition function - $\varepsilon$-probability of hypervolume improvement ($\varepsilon$-PoHVI). Experimentally, we show that on many widely-applied bi-objective test problems, $\varepsilon$-PoHVI significantly outperforms other related acquisition functions, e.g., $\varepsilon$-PoI, and expected hypervolume improvement, when the GP model exhibits a large the prediction uncertainty.
