Gaussian processes are only one implementation of Bayesian optimization- afaict, you have created another using a different prior which has nicer computational

Gaussian processes are only one implementation of Bayesian optimization- afaict, you have created another using a different prior which has nicer computational properties, mostly due to assuming the function has little global structure, a reasonable one for tricky optimization problems. I wonder how it would compare to a GP approximation using a space-partitioning data structure, only considering nearby points when calculating sample utility.