Interpretable reinforcement learning policies are essential for high-stakes decisionmaking, yet optimizing decision tree policies in Markov Decision Processes (MDPs) remains challenging. We propose SPOT, a novel method for computing decision tree policies, which formulates the optimization problem as a mixedinteger linear program (MILP). To enhance efficiency, we employ a reduced-space branch-and-bound approach that decouples the MDP dynamics from tree-structure constraints, enabling efficient parallel search. This significantly improves runtime and scalability compared to previous methods. Our approach ensures that each iteration yields the optimal decision tree. Experimental results on standard benchmarks demonstrate that SPOT achieves substantial speedup and scales to larger MDPs with a significantly higher number of states. The resulting decision tree policies are interpretable and compact, maintaining transparency without compromising performance. These results demonstrate that our approach simultaneously achieves interpretability and scalability, delivering high-quality policies an order of magnitude faster than existing approaches.

We propose a simple generalization of standard and empirically successful decision tree learning algorithms such as ID3, C4.5, and CART. These 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. Our 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 greediness hierarchy theorem showing that for every k N, Top-(k +1) can be dramatically more powerful than Top-k: there are data distributions for which the former achieves accuracy 1 ε, whereas the latter only achieves accuracy 12 +ε. We then show, through extensive experiments, that Top-k outperforms 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 greedy algorithms across a wide range of benchmarks. 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 far beyond the reach of these algorithms.

Decision trees are a fundamental workhorse in machine learning. Their logical and hierarchical structure makes them easy to understand and their predictions easy to explain.

Dynamic programming methods have been shown to scale much better because they exploit the tree structure by solving subtrees as independent subproblems.

A fundamental task in active learning involves performing a sequence of tests to identify an unknown hypothesis that is drawn from a known distribution. This problem, known as optimal decision tree induction, has been widely studied for decades and the asymptotically best-possible approximation algorithm has been devised for it. We study a generalization where certain test outcomes are noisy, even in the more general case when the noise is persistent, i.e., repeating the test on the scenario gives the same noisy output, disallowing simple repetition as a way to gain confidence. We design new approximation algorithms for both the non-adaptive setting, where the test sequence must be fixed a-priori, and the adaptive setting where the test sequence depends on the outcomes of prior tests. Previous work in the area assumed at most a constant number of noisy outcomes per test and per scenario and provided approximation ratios that were problem dependent (such as the minimum probability of a hypothesis). Our new approximation algorithms provide guarantees that are nearly best-possible and work for the general case of a large number of noisy outcomes per test or per hypothesis where the performance degrades smoothly with this number. Our results adapt and generalize methods used for submodular ranking and stochastic set cover. We evaluate the performance of our algorithms on two natural applications with noise: toxic chemical identification and active learning of linear classifiers. Despite our logarithmic theoretical approximation guarantees, our methods give solutions with cost very close to the information theoretic minimum, demonstrating the effectiveness of our methods.

Global optimization of decision trees has shown to be promising in terms of accuracy, size, and consequently human comprehensibility. However, many of the methods used rely on general-purpose solvers for which scalability remains an issue.Dynamic programming methods have been shown to scale much better because they exploit the tree structure by solving subtrees as independent subproblems. However, this only works when an objective can be optimized separately for subtrees.We explore this relationship in detail and show the necessary and sufficient conditions for such separability and generalize previous dynamic programming approaches into a framework that can optimize any combination of separable objectives and constraints.Experiments on five application domains show the general applicability of this framework, while outperforming the scalability of general-purpose solvers by a large margin.