I need to solve an optimization problem based on a function f(X). This function is not known, but it can be estimated from a training set. So first I train a model, then I get the score function f(X), and then I can use this function to solve my optimization problem.
So far, in my problem, I used a simple polynomial regression, and hence the score function is a polynomial. With this score function, the optimization problem works very well since it is infinitely derivable.
Now I want to improve f using a more complex model, i.e. a classic neural network for regression. I wonder: what kind of properties does the score function have in neural networks? Is it at least continuous? Is it derivable?