I am looking for a statistical method (and a link to a nice R package would be cool too!) which allows me to find which point to evaluate next for a given function.
I have a non-stochastic function z := f(x, y), which can be evaluated for given x, y pairs. Evaluation is expensive so I want to optimize which points to evaluate next to reduce number of function calls.
My goal is to get a good approximation of the surface of z over the grid of possible x and y values and not like many optimization methods only find the maximum (or minimum) value.
So basically I need to define some objective function that tells me that points far away from previously evaluated points and regions with a high variation in z should be prioritized, while regions in which z is nearly constant and close to previously evaluated points should have a low priority. So a combination of distance and variation and then find the maximum of this function, which is then the next point to evaluate z on.
Gaussian Processes / Bayesian Optimization could be fitting, but I am not sure how exactly I can make it work in my example.