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

Learning How to Optimize Black-Box Functions With Extreme Limits on the Number of Function Evaluations