Most research in Bayesian optimization (BO) has focused on direct feedback scenarios, where one has access to exact, or perturbed, values of some expensive-to-evaluate objective. This direction has been mainly driven by the use of BO in machine learning hyper-parameter configuration problems. However, in domains such as modelling human preferences, A/B tests or recommender systems, there is a need of methods that are able to replace direct feedback with preferential feedback, obtained via rankings or pairwise comparisons. In this work, we present Preferential Batch Bayesian Optimization (PBBO), a new framework that allows to find the optimum of a latent function of interest, given any type of parallel preferential feedback for a group of two or more points. We do so by using a Gaussian process model with a likelihood specially designed to enable parallel and efficient data collection mechanisms, which are key in modern machine learning. We show how the acquisitions developed under this framework generalize and augment previous approaches in Bayesian optimization, expanding the use of these techniques to a wider range of domains. An extensive simulation study shows the benefits of this approach, both with simulated functions and four real data sets.

Bayesian optimization (BO) is a global optimization strategy designed to find the minimum of an expensive black-box function, typically defined on a compact subset of R d , by using a Gaussian process (GP) as a surrogate model for the objective. Although currently available acquisition functions address this goal with different degree of success, an over-exploration effect of the contour of the search space is typically observed. However, in problems like the configuration of machine learning algorithms, the function domain is conservatively large and with a high probability the global minimum does not sit on the boundary of the domain. We propose a method to incorporate this knowledge into the search process by adding virtual derivative observations in the GP at the boundary of the search space. We use the properties of GPs to impose conditions on the partial derivatives of the objective. The method is applicable with any acquisition function, it is easy to use and consistently reduces the number of evaluations required to optimize the objective irrespective of the acquisition used. We illustrate the benefits of our approach in an extensive experimental comparison.

The increasing availability of structured but high dimensional data has opened new opportunities for optimization. One emerging and promising avenue is the exploration of unsupervised methods for projecting structured high dimensional data into low dimensional continuous representations, simplifying the optimization problem and enabling the application of traditional optimization methods. However, this line of research has been purely methodological with little connection to the needs of practitioners so far. In this article, we study the effect of different search space design choices for performing Bayesian optimization in high dimensional structured datasets. In particular, we analyses the influence of the dimensionality of the latent space, the role of the acquisition function and evaluate new methods to automatically define the optimization bounds in the latent space. Finally, based on experimental results using synthetic and real datasets, we provide recommendations for the practitioners.

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Drug development commonly studies an adult population first and then the pediatric population. The knowledge from the adult population is taken advantage of for the design of the pediatric trials. Adjusted drug doses for these are often derived from adult pharmacokinetic (PK) models which are extrapolated to patients with smaller body size. This extrapolation is based on scaling physiologic model parameters with a body size measure accounting for organ size differences. The inherent assumption is that children are merely small adults. However, children can be subject to additional effects such as organ maturation. These effects are not present in the adult population and are possibly overlooked at the design stage of the pediatric trials. It is thus crucial to qualify the extrapolation assumptions once the pediatric trial data are available. In this work, we propose a model based on a non‐parametric regression method called Gaussian process (GP) to detect deviations from the made extrapolation assumptions. We introduce the theoretical background of this model and compare its performance to a parametric expansion of the adult model. The comparison includes simulations and a clinical study data example. The results show that the GP approach can reliably detect maturation trends from sparse pediatric data.