Research under this award designed new Bayesian optimization (BayesOpt) methods that better optimize slow-to-evaluate black-box functions. The mathematical tools created by this research support better decisions in medicine, materials science, transportation, logistics, e-commerce, aerospace, and neural network design. This research also contributed to the creation of a startup company, SigOpt, which provides enterprise BayesOpt software. This research has also has been incorporated into two widely used open-source BayesOpt software packages, Yelp's Metrics Optimization Engine and Facebook's BoTorch.

To illustrate the optimization problems considered by this award, consider using a patient-specific cardiovascular simulator to support coronary bypass surgery. The long-term success of the surgery (the "objective function", or "objective") as predicted by the simulator depends on the design of the bypass graft: the position and angle at which each end of the graft attaches to the artery. We can evaluate graft designs in the simulator and use the best one evaluated in surgery.

Unfortunately, complex simulators often require hours of computer time per evaluation. This and a deadline on graft selection limits the number of evaluations we can perform. As a result, we can evaluate only a small fraction of the search space, potentially missing the best designs.

Compounding the challenge, a complex simulator's output often depends on its input in a non-convex "bumpy" way. Classical hill-climbing approaches may get stuck on a solution that is substantially worse than the global best. Moreover, complex simulators often do not calculate derivatives, requiring such hill-climbing approaches to use many simulator evaluations to approximate them. Black-box methods like genetic algorithms deal well with non-convex objective functions and do not require derivatives but typically require too many evaluations for slow-to-evaluate simulators.

This award developed new BayesOpt methods for optimizing functions calculated by cardiovascular bypass graft simulators and other complex slow-to-evaluate non-convex functions. They can also be used to optimize functions that are evaluated using physical experiments, as in materials design and drug discovery.

BayesOpt uses machine learning to predict the objective function at unevaluated inputs. It then uses this prediction (with uncertainty) to define an "acquisition function" quantifying the value of the information from evaluating the objective function at a new point. By evaluating at points providing the most valuable information (which can be found efficiently because acquisition functions often evaluate quickly and provide derivatives) we can find a good solution to our optimization problem with few evaluations. The figure illustrates this.

Intellectual Merit: The research supported by this award has created new methods and analyses for BayesOpt and two other closely-related problems: multi-armed bandits and ranking and selection. Highlights include:

• Grey-box BayesOpt: Historically, BayesOpt has treated the objective function as a black box. This research showed that query efficiency can be substantially improved by "looking inside the box", i.e., by using knowledge of how the objective function is computed. This research developed grey-box methods for these settings: objectives with derivative observations; objectives that are sums or integrals of the outputs of a slow-to-evaluate black box function; objectives that are compositions of a known function and a vector-valued black box function (important in simulator calibration and inverse reinforcement learning); and objective functions that produce "traces", i.e., timeseries that converge to the objective function value, as produced in neural network design.
• Parallel BayesOpt: This research developed a new efficient approach to optimizing Monte Carlo acquisition functions. This enabled development of two new query-efficient parallel BayesOpt methods now widely used in practice.
• Multi-Information Source BayesOpt: Multi-information source optimization (MISO) leverages other sources of information that are faster to evaluate than our objective but provide noisy biased estimates. For example, when optimizing a prediction from a partial differential equation, we may predict more quickly but less accurately using a coarser mesh or a simpler partial differential equation. This research developed new BayesOpt methods for MISO.
• Large-scale Ranking and Selection (R&S): This research developed new R&S methods that have theoretical performance guarantees and scale to large problems.

Broader Impact: The research in this award has led to applied work with broader impact in materials science, transportation, e-commerce, finance, aerospace, and neural network design. This impact has arisen directly through the PI and others using the methods developed and through the broader application of BayesOpt facilitated by the software development (Metrics Optimization Engine, BoTorch) and startup company (SigOpt) resulting from this research and from a widely read tutorial article written by the PI and an associated video.

Methods, examples, and insights from this research were incorporated into several courses taught at Cornell: ORIE 3120 "Practical Tools in Operations Research, Machine Learning and Data Science"; ORIE 6750 "Optimal Learning"; and a 1-week computational laboratory focused on optimization in medical decision-making and healthcare operations for female high school students within Cornell's CURIE Academy summer program. This research also provided training opportunities for 13 PhD students, 1 Masters student, and 10 undergraduates.

Last Modified: 03/26/2020
Modified by: Peter I Frazier