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

Emmanuel Vazquez, Sébastien Petit

We study the expected improvement (EI) policy for minimizing a deterministic objective function $f$ on a nonempty compact set $\mathcal{X}\subset {\mathbb{R}}^d$. We assume that $f$ be…