  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.
