Decision tree learning is a widely used approach in machine learning,
favoured in applications that require concise and interpretable models.
Heuristic methods are traditionally used to quickly produce models with
reasonably high accuracy. A commonly criticised point, however, is that the
resulting trees may not necessarily be the best representation of the data in
terms of accuracy and size. In recent years, this motivated the development of
optimal classification tree algorithms that globally optimise the decision tree
in contrast to heuristic methods that perform a sequence of locally optimal
decisions. We follow this line of work and provide a novel algorithm for
learning optimal classification trees based on dynamic programming and search.
Our algorithm supports constraints on the depth of the tree and number of
nodes. The success of our approach is attributed to a series of specialised
techniques that exploit properties unique to classification trees. Whereas
algorithms for optimal classification trees have traditionally been plagued by
high runtimes and limited scalability, we show in a detailed experimental study
that our approach uses only a fraction of the time required by the
state-of-the-art and can handle datasets with tens of thousands of instances,
providing several orders of magnitude improvements and notably contributing
towards the practical realisation of optimal decision trees.

本研究提出了一种基于动态规划和搜索的学习算法来实现最优决策树，这种算法支持对树的深度和节点数量设置限制，并在实验证明使用我们的算法只需要很短的时间就可以处理具有成千上万个实例的数据集，从而极大地提高了最优决策树的实用性。