I have a complicated loss function a(x, y) that takes a long time to compute. But I have 2 similar loss functions b(x, y) and c(x, y) that each capture some aspects of a(x, y).
How could I easiest find f() and g() such that a(x, y) = f(b(x, y)) + g(c(x, y))?
I can sample any data x, y to try these functions. Would I do some curve fitting or evolutionary coding to get somewhere? I can try guessing but that will only get me so far.
Here are some quick values from inserting semi-arbitrary values to a, b, and c:
