Supplementary Materials A Constraint Explanation for Problem 2 Constraint 2b checks the loss of each sample and the derivation is shown as follows

Constraint 2b checks the loss of each sample and the derivation is shown as follows. Constraint 2d to 2i are mainly adopted from Bertsimas and Dunn [2019] on Chapter 8.2. Here we briefly explain the meaning and derivations of these constraints. Constraint 2g and 2h are set to ensure that if there's no split on Constraint 2i enforces the hierarchical structure of the tree. Algorithm 1 depicts the details of the Branch-and-bound scheme for training the optimal decision tree.