Decision Trees (DTs) are commonly used for many machine learning tasks due to their high degree of interpretability. However, learning a DT from data is a difficult optimization problem, as it is non-convex and non-differentiable. Therefore, common approaches learn DTs using a greedy growth algorithm that minimizes the impurity locally at each internal node. Unfortunately, this greedy procedure can lead to inaccurate trees. In this paper, we present a novel approach for learning hard, axis-aligned DTs with gradient descent. The proposed method uses backpropagation with a straight-through operator on a dense DT representation, to jointly optimize all tree parameters. Our approach outperforms existing methods on binary classification benchmarks and achieves competitive results for multi-class tasks.

翻译：决策树因其高度可解释性而被广泛应用于许多机器学习任务中。然而，从数据中学习决策树是一个困难的优化问题，因为它具有非凸和非可微的性质。因此，常见方法采用贪心增长算法来构建决策树，该算法在每个内部节点局部最小化不纯度。遗憾的是，这种贪心过程可能导致不准确的树结构。本文提出了一种新颖方法，使用梯度下降学习硬性轴对齐决策树。该方法利用密集决策树表示上的直通算子进行反向传播，从而联合优化所有树参数。我们的方法在二分类基准测试中优于现有方法，并在多分类任务中取得了具有竞争力的结果。