Part 2 · Intuition
The loop: model, decide, evaluate, repeat
fit surrogateGP posterior over f
from all data so far
→
from all data so far
optimize acquisitionthousands of cheap queries
on the model
→
on the model
evaluate fthe one expensive step
→
augment dataand loop
One iteration of Bayesian optimization. Note the asymmetry: the inner
optimization (of the acquisition function) is hammered with thousands of evaluations precisely
because they cost nothing — all the expense is quarantined in one red box.
Two functions are being optimized, and confusing them is the classic beginner error. The acquisition function is optimized every iteration, cheaply, on the surrogate. The objective f is only ever evaluated at the acquisition’s single chosen point. BO is a machine for converting cheap model computation into expensive-evaluation frugality.
Definition. Bayesian optimization is sequential optimization of an expensive black-box function in which a Bayesian surrogate model (usually a Gaussian process) supplies a posterior belief over f, and an acquisition function maps that belief — both its predictions and its uncertainties — to the choice of the next evaluation point.