Many scientific and industrial applications require the joint optimization of multiple, potentially competing objectives. Multi-objective Bayesian optimization (MOBO) is a sample-efficient framework for identifying Pareto-optimal solutions. At the heart of MOBO is the acquisition function, which determines the next candidate to evaluate by navigating the best compromises among the objectives. In this paper, we show a natural connection between non-dominated solutions and the extreme quantile of the joint cumulative distribution function (CDF). Motivated by this link, we propose the Pareto-compliant CDF indicator and the associated acquisition function, BOtied. BOtied inherits desirable invariance properties of the CDF, and an efficient implementation with copulas allows it to scale to many objectives. Our experiments on a variety of synthetic and real-world problems demonstrate that BOtied outperforms state-of-the-art MOBO acquisition functions while being computationally efficient for many objectives.

翻译：许多科学和工业应用需要同时优化多个可能相互竞争的目标。多目标贝叶斯优化是一种用于识别帕累托最优解的样本高效框架。其核心是采集函数，它通过权衡各目标之间的最佳折中来确定下一个待评估候选点。本文揭示了非支配解与联合累积分布函数极端分位数之间的自然联系。基于这一关联，我们提出了帕累托一致的CDF指标及其对应的采集函数BOtied。BOtied继承了CDF的理想不变性特性，并通过copula实现高效扩展以适用于多目标场景。在多种合成与真实问题上的实验表明，BOtied在保持多目标计算高效性的同时，性能优于当前最先进的多目标贝叶斯优化采集函数。