BOtied: Multi-objective Bayesian optimization with tied multivariate ranks

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.