Many scientific and industrial applications require joint optimization of multiple, potentially competing objectives. Multi-objective Bayesian optimization (MOBO) is a sample-efficient framework for identifying Pareto-optimal solutions. We show a natural connection between non-dominated solutions and the highest multivariate rank, which coincides with the outermost level line of the joint cumulative distribution function (CDF). We propose the CDF indicator, a Pareto-compliant metric for evaluating the quality of approximate Pareto sets that complements the popular hypervolume indicator. At the heart of MOBO is the acquisition function, which determines the next candidate to evaluate by navigating the best compromises among the objectives. Multi-objective acquisition functions that rely on box decomposition of the objective space, such as the expected hypervolume improvement (EHVI) and entropy search, scale poorly to a large number of objectives. We propose an acquisition function, called BOtied, based on the CDF indicator. BOtied can be implemented efficiently with copulas, a statistical tool for modeling complex, high-dimensional distributions. We benchmark BOtied against common acquisition functions, including EHVI and random scalarization (ParEGO), in a series of synthetic and real-data experiments. BOtied performs on par with the baselines across datasets and metrics while being computationally efficient.

翻译：许多科学与工业应用需要联合优化多个可能相互冲突的目标。多目标贝叶斯优化（MOBO）是一种识别帕累托最优解的样本高效框架。我们揭示了非支配解与最高多元秩之间的自然联系，该秩恰好对应联合累积分布函数（CDF）的最外层等高线。我们提出CDF指标，一种用于评估近似帕累托集质量的帕累托兼容度量，可补充广泛使用的超体积指标。MOBO的核心是采集函数，它通过权衡目标间的最佳折衷来确定下一个待评估候选点。依赖目标空间箱式分解的多目标采集函数（如期望超体积改进EHVI和熵搜索方法）在目标数量较多时扩展性较差。我们基于CDF指标提出名为BOtied的采集函数，该函数可通过Copula——一种用于建模复杂高维分布的统计工具——高效实现。在系列合成与真实数据实验中，我们将BOtied与EHVI和随机标量化（ParEGO）等常见采集函数进行基准测试。结果表明，BOtied在跨数据集与指标维度上性能与基线方法相当，同时保持计算效率。