Abstract
We give strengthened provable guarantees on the performance of widely employed and empirically successful {\sl top-down decision tree learning heuristics}. While prior works have focused on the realizable setting, we consider the more realistic and challenging {\sl agnostic} setting. We show that for all monotone functions~f and parameters s∈ N, these heuristics construct a decision tree of size s^O((log s)/ε²) that achieves error ≤ opt_s + ε, where opt_s denotes the error of the optimal size-s decision tree for f. Previously, such a guarantee was not known to be achievable by any algorithm, even one that is not based on top-down heuristics. We complement our algorithmic guarantee with a near-matching s^Ω(log s) lower bound.