# What is minimized/optimized when we use AdaBoost

When I learned about CART, we learned that at each split, we try to minimize some measure (usually Gini index) of the split. That is, we determine the predictor and threshold that decreases the Gini index the most.

I am reading about the AdaBoost model and am not seeing the criteria used to determine the splits and how it factors in our weighted observations. I'm assuming we no longer use the Gini index?

To determine a split, do we just minimize the weighted sum of the weighted error rate? Do we pick the split the decreases the weighted error rate the most? Per AdaBoost, the weighted error rate is calculated as:

Let's say the two child nodes have a total of 20 observations. Let's say the left node (L) has m observations and thus the right node (R) has (20 - m) observations. Do we determine the split that minimizes:

m/20 * err(L) + (20 - m)/20 * err(R)

where L and R are the left and right child nodes and err(L) is the error rate of the left child node using the formula given by AdaBoost?