Rolling lookahead learning for optimal classification trees

Classification trees continue to be widely adopted in machine learning applications due to their inherently interpretable nature and scalability. We propose a rolling subtree lookahead algorithm that combines the relative scalability of the myopic approaches with the foresight of the optimal approaches in constructing trees. The limited foresight embedded in our algorithm aims to address potential learning pathology that may arise in optimal approaches. At the heart of our algorithm lies a novel two-depth optimal binary classification tree formulation flexible to handle any loss function. We show that the feasible region of this formulation is an integral polyhedron, yielding the LP relaxation solution optimal. Through extensive computational analyses, we demonstrate that our approach achieves better performance than existing optimization based solutions, which are subject to practical computational limitations, and computationally efficient myopic approaches in 981 out of 1610 problem instances, improving the out-of-sample accuracy by up to 14.4% and 23.6%, respectively.