Simple-regret rates and minimax optimality of fixed-prior expected improvement in Matérn and squared-exponential RKHSs

Emmanuel Vazquez, Sébastien Petit

We study expected improvement (EI) for minimizing a deterministic function $f$ in the RKHS ${\mathcal{H}}_k$ of a continuous positive-semidefinite kernel $k$ on a nonempty compact set…