In the paper 'Algorithms for Hyper-Parameter Optimization' (pdf), where they explain the 'Sequential Model-based Global optimization method (SMBO)', the authors made a comment that,
SMBOalgorithms differ in what criterion they use to obtain the next candidate of hyper-parameters given a model (or surrogate of the expensive model $f$), and in model $f$ via observation history.
I unable to wrap my head around the need of criterion why not just use the best set of hyper-parameter that gives the best result for the surrogate of $f$. Elaborated, as author uses Gaussian processes as a surrogate - why you require criterion instead of querying for all candidate which is likely to improve just like in Gaussian regression.
Note: Here, SMBO refers to a method where hyper-parameters are being tuned for a given model $f$ when training operation is very expensive. In SMBO, a surrogate model of $f$ is used as it would be cheaper to train and thereby increase the hyper-parameter tuning operation.