  We consider black-box optimization in which only an extremely limited number
of function evaluations, on the order of around 100, are affordable and the
function evaluations must be performed in even fewer batches of a limited
number of parallel trials. This is a typical scenario when optimizing variable
settings that are very costly to evaluate, for example in the context of
simulation-based optimization or machine learning hyperparameterization. We
propose an original method that uses established approaches to propose a set of
points for each batch and then down-selects from these candidate points to the
number of trials that can be run in parallel. The key novelty of our approach
lies in the introduction of a hyperparameterized method for down-selecting the
number of candidates to the allowed batch-size, which is optimized offline
using automated algorithm configuration. We tune this method for black box
optimization and then evaluate on classical black box optimization benchmarks.
Our results show that it is possible to learn how to combine evaluation points
suggested by highly diverse black box optimization methods conditioned on the
progress of the optimization. Compared with the state of the art in black box
minimization and various other methods specifically geared towards few-shot
minimization, we achieve an average reduction of 50\% of normalized cost, which
is a highly significant improvement in performance.
