When is Non-Stochastic Global Optimization Preferable or Necessary?
Non-stochastic global optimization could be practical for the directed search of the solution space. If there is a priori knowledge, that knowledge can direct the optimization to specific regions. Stochastic global optimization might explore inefficiently explore regions of the solution space.
A specific example of non-stochastic global optimization is Bayesian optimization. In Bayesian optimization, samples are not picked at random. Samples are picked based the calculated posterior distribution, often to maximize the expected improvement.
Bayesian optimization has been used in many applications, including machine learning hyperparameter tuning.