How hard can it be to wrap it in a loop and apply some off-the-shelf good old fashioned AI^H^H optimization technique?
"Given specific inputs X and outputs Y, have a computer automatically find modifications to F so that F(X) gives Y" is a problem that's been studied for nearly a century now (longer, if relax the meaning of "computer"), with plenty of well-known solutions, most of which don't require F to be differentiable.
Isn't "operational research" a standard part of undergrad CS curriculum? It was at my alma mater.
