Learning Optimal Classification Trees: Strong Max-Flow Formulations
This work addresses the suboptimality and inefficiency of existing methods for binary classification trees, offering significant speed and performance gains, though it is incremental as it builds on prior MIP-based techniques.
The authors tackled the problem of learning optimal binary classification trees by proposing a flow-based mixed-integer programming formulation with a stronger linear programming relaxation, resulting in approaches that are 50 times faster than state-of-the-art methods and improve out-of-sample performance by up to 13.8%.
We consider the problem of learning optimal binary classification trees. Literature on the topic has burgeoned in recent years, motivated both by the empirical suboptimality of heuristic approaches and the tremendous improvements in mixed-integer programming (MIP) technology. Yet, existing approaches from the literature do not leverage the power of MIP to its full extent. Indeed, they rely on weak formulations, resulting in slow convergence and large optimality gaps. To fill this gap in the literature, we propose a flow-based MIP formulation for optimal binary classification trees that has a stronger linear programming relaxation. Our formulation presents an attractive decomposable structure. We exploit this structure and max-flow/min-cut duality to derive a Benders' decomposition method, which scales to larger instances. We conduct extensive computational experiments on standard benchmark datasets on which we show that our proposed approaches are 50 times faster than state-of-the art MIP-based techniques and improve out of sample performance up to 13.8%.