Non-linear Regression

Question

For example suppose I've data set which looks like:

[[x,y,z],
 [1,2,5],
 [2,3,8],
 [4,5,14]]

It's easy to find the theta parameters from those tiny data set. Which is theta = [1,2,0]

z = 1*x + 2*y + 0 

But if my data set are non linear. Suppose:

[[x,y,z],
 [1,2,6],
 [2,3,15]]]

If i choose the mapping function to be of: z = xy+yy

It would return the theta parameter :

theta = [1,1,0]

So my deal is how to choose such mapping function for data sets which varies over time. As in recommender system the user rating varies as per the time, to reduce the cost. I've recently gone through regularization. Is there any other ideas for reducing the cost.