We consider the problem of adaptively placing sensors along an interval to detect stochastically-generated events. We present a new formulation of the problem as a continuum-armed bandit problem with feedback in the form of partial observations of realisations of an inhomogeneous Poisson process. We design a solution method by combining Thompson sampling with nonparametric inference via increasingly granular Bayesian histograms and derive an $\tilde{O}(T^{2/3})$ bound on the Bayesian regret in $T$ rounds. This is coupled with the design of an efficent optimisation approach to select actions in polynomial time. In simulations we demonstrate our approach to have substantially lower and less variable regret than competitor algorithms.

Automatic Chemical Design leverages recent advances in deep generative modelling to provide a framework for performing continuous optimization of molecular properties. Although the provision of a continuous representation for prospective lead drug candidates has opened the door to hitherto inaccessible tools of mathematical optimization, some challenges remain for the design process. One known pathology is the model's tendency to decode invalid molecular structures. The goal of this thesis is to test the hypothesis that the origin of this pathology is rooted in the current formulation of Bayesian optimization. Recasting the optimization procedure as a constrained Bayesian optimization problem results in novel drug compounds produced by the model consistently ranking in the 100th percentile of the distribution over training set scores.