Bayesian Optimization
Choosing where to evaluate an expensive function next by fitting a surrogate model to past evaluations and ranking candidates with an acquisition function.
A Gaussian process is the usual surrogate: it predicts both a value and an uncertainty at any point, tight near past evaluations and wide everywhere else. Expected improvement, the most common acquisition function, ranks a candidate high when the surrogate predicts a good result, high uncertainty, or both, balancing exploring the unknown against exploiting what already looks promising.
The overhead only pays off when a real evaluation is expensive, like a full training run; for anything fast to evaluate, plain random search usually wins on wall-clock time.