For both the RBF and the Matèrn-3/2 kernels, we consider three possible ranges of lengthscales, including [0.07,0.13],[0.17,0.23],[0.27,0.33]. Forbothtraining andthefastadaptation during testing, weapply 5-shot adaptation (i.e., 5black-box functions areused foradaptation) and set the number offew-shot gradient updates tobe5. Specifically, the amount of translation added to each dimension ofx is selected from the range [ 0.1xlim,0.1xlim]uniformly To address the continuous input domains and achieve a fair comparison between FSAF and MetaBO, we leverage the hierarchical gridding method similar to that in [27] for the maximization procedure of the AFs. The validation set is used for both few-shot adaptation of FSAF as well as finding the lengthscale parameter of the GP surrogate modelforposteriorinference.

Bayesian optimization (BO) conventionally relies on handcrafted acquisition functions (AFs) to sequentially determine the sample points. However, it has been widely observed in practice that the best-performing AF in terms of regret can vary significantly under different types of black-box functions. It has remained a challenge to design one AF that can attain the best performance over a wide variety of black-box functions.

The main result is informally presented here.

The main result is informally presented here.