Title: The power of choices in decision tree learning. Abstract: We propose a simple and natural generalization of standard and empirically successful decision tree learning algorithms such as ID3, C4.5, and CART.   These classic algorithms, which have been central to machine learning for decades, are greedy in nature: they grow a decision tree by iteratively splitting on the "best" attribute.  We augment these algorithms with an additional greediness parameter $k$ and our resulting algorithm, Top-$k$, considers the $k$ best attributes as possible splits instead of just the single best attribute.

We demonstrate, theoretically and empirically, the power of this  simple generalization.  We first prove a sharp greediness hierarchy theorem showing that for every $k\in \mathbb{N}$, Top-$(k+1)$  can be much more powerful than Top-$k$: there are data distributions for which the former achieves accuracy $1-\epsilon$, whereas the latter only achieves accuracy $\frac{1}{2}+\epsilon$.  We then show, through extensive experiments, that Top-$k$ compares favorably with the two main approaches to decision tree learning: classic greedy algorithms and more recent "optimal decision tree" algorithms.  On one hand, Top-$k$ consistently enjoys significant accuracy gains over the greedy algorithms across a wide range of benchmarks, at the cost of only a mild training slowdown.  On the other hand, Top-$k$ is markedly more scalable than optimal decision tree algorithms, and is able to handle dataset and feature set sizes that remain beyond the reach of these algorithms.  

Taken together, our results highlight the  potential practical impact of the power of choices in decision tree learning.