The geometry of Gaussian processes and Bayesian optimization

In this talk we analyse Bayesian optimization in light of the geometry of Gaussian processes for their canonical distance. I will use the chaining trick to derive upper and lower bounds on the supremum of the process. I will then present an adaptive optimization algorithm that uses a discretization tree built with chaining, and show theoretical guarantees as well as numerical experiments. Finally we will see connexions with tree-based algorithms like DOO and related approaches.