# Gradient descent with no analytical function f(x)

I find myself in the position of wanting to minimize a numerical function f(a,b) with respect to a and b for which I do not have a the analytical form f(a,b). All I have is f(a,b) for many values of a and b. Is it still possible to do a gradient descent to minimize f with respect to a and b?

$$w_{k+1} = w_{k} - \alpha_{k} \nabla f(w)$$

with w the vector holding a and b.

Or is numerical gradient descent impossible?

• Can you calculate gradients of $f$ with respect to parameters? If no, then you are missing the key component. – Tim Mar 25 '19 at 21:30

You also need to be able to find new values of $$f(a,b)$$. If you can't do that, your best guess at optimising $$f$$ is taking the minimum value for $$f$$ that you've found so far. (Unless of course the values for $$f$$ can be clearly and unambiguously extrapolated from the data you already have.)