  The Classification Tree (CT) is one of the most common models in
interpretable machine learning. Although such models are usually built with
greedy strategies, in recent years, thanks to remarkable advances in
Mixer-Integer Programming (MIP) solvers, several exact formulations of the
learning problem have been developed. In this paper, we argue that some of the
most relevant ones among these training models can be encapsulated within a
general framework, whose instances are shaped by the specification of loss
functions and regularizers. Next, we introduce a novel realization of this
framework: specifically, we consider the logistic loss, handled in the MIP
setting by a linear piece-wise approximation, and couple it with
$\ell_1$-regularization terms. The resulting Optimal Logistic Tree model
numerically proves to be able to induce trees with enhanced interpretability
features and competitive generalization capabilities, compared to the
state-of-the-art MIP-based approaches.
