Decision Tree Learning is a fundamental problem for Interpretable Machine Learning, yet it poses a formidable optimization challenge. Despite numerous efforts dating back to the early 1990's, practical algorithms have only recently emerged, primarily leveraging Dynamic Programming (DP) and Branch & Bound (B&B) techniques. These breakthroughs led to the development of two distinct approaches. Algorithms like DL8.5 and MurTree operate on the space of nodes (or branches), they are very fast, but do not penalise complex Decision Trees, i.e. they do not solve for sparsity. On the other hand, algorithms like OSDT and GOSDT operate on the space of Decision Trees, they solve for sparsity but at the detriment of speed. In this work, we introduce Branches, a novel algorithm that integrates the strengths of both paradigms. Leveraging DP and B&B, Branches achieves exceptional speed while also solving for sparsity. Central to its efficiency is a novel analytical bound enabling substantial pruning of the search space. Theoretical analysis demonstrates that Branches has lower complexity compared to state-of-the-art methods, a claim validated through extensive empirical evaluation. Our results illustrate that Branches not only greatly outperforms existing approaches in terms of speed and number of iterations, it also consistently yields optimal Decision Trees.

Branches算法结合了动态规划和分支界限方法，提供了出色的速度和稀疏性解决方案，通过理论分析和实证评估验证了比现有方法更低复杂性以及始终产生最优的决策树的优势。

分支：用于优化决策树的快速动态规划和分支限界算法