BOtied: Multi-objective Bayesian optimization with tied multivariate ranks

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.Comment: 10 pages (+5 appendix), 9 figures. Submitted to NeurIP

Multi-Fidelity Bayesian Optimization for Efficient Materials Design

Materials design is a process of identifying compositions and structures to achieve desirable properties. Usually, costly experiments or simulations are required to evaluate the objective function for a design solution. Therefore, one of the major challenges is how to reduce the cost associated with sampling and evaluating the objective. Bayesian optimization is a new global optimization method which can increase the sampling efficiency with the guidance of the surrogate of the objective. In this work, a new acquisition function, called consequential improvement, is proposed for simultaneous selection of the solution and fidelity level of sampling. With the new acquisition function, the subsequent iteration is considered for potential selections at low-fidelity levels, because evaluations at the highest fidelity level are usually required to provide reliable objective values. To reduce the number of samples required to train the surrogate for molecular design, a new recursive hierarchical similarity metric is proposed. The new similarity metric quantifies the differences between molecules at multiple levels of hierarchy simultaneously based on the connections between multiscale descriptions of the structures. The new methodologies are demonstrated with simulation-based design of materials and structures based on fully atomistic and coarse-grained molecular dynamics simulations, and finite-element analysis. The new similarity metric is demonstrated in the design of tactile sensors and biodegradable oligomers. The multi-fidelity Bayesian optimization method is also illustrated with the multiscale design of a piezoelectric transducer by concurrently optimizing the atomic composition of the aluminum titanium nitride ceramic and the device’s porous microstructure at the micrometer scale.Ph.D