BOtied: Multi-objective Bayesian optimization with tied multivariate ranks
Primary Area: probabilistic methods (Bayesian methods, variational inference, sampling, UQ, etc.)
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Keywords: Bayesian optimization, multi-objective optimization, density estimation, copulas
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TL;DR: We propose a robust acquisition function for multi-objective Bayesian optimization.
Abstract: 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. 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 begin by showing 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). Motivated by this link, we propose the CDF indicator, a Pareto-compliant metric for evaluating the quality of approximate Pareto sets that complements the popular hypervolume indicator. We then propose an acquisition function based on the CDF indicator, called BOtied. 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, entropy search, and random scalarization, in a series of synthetic and real-data experiments. BOtied performs on par with the baselines across datasets and metrics while being computationally efficient.
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Submission Number: 6099
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