Finding the smallest decision tree that perfectly fits the training data is NP-complete; yet, such trees remain attractive due to their interpretability and minimal footprint. Existing solutions occupy two extremes: heuristics like CART instantly produce trees but remain far from optimal, whereas exact solvers like Witty give no intermediate output. We introduce AnyDTree, an anytime algorithm that continuously maintains a 100% accurate tree and monotonically shrinks its size. It employs an expand-and-backtrack search that ensures complete solutions at every step, combined with aggressive pruning and caching mechanisms to eliminate redundant exploration. On 70 binary-classification variants of 35 UCI datasets, AnyDTree incurs no statistically significant overhead in finding the optimal size compared with Witty (log-rank p>0.1). On the 46 datasets with known optima, it demonstrates significantly improved anytime behaviour - measured by the confined primal integral - with a median score of 0.00034, outperforming both Witty (0.00059) and CART (0.20) (p<0.001). These results position AnyDTree as a practical middle ground between heuristic and exact solutions.

Interpretability distinguishes decision trees from most other machine learning models; what they still have in common is that they are vulnerable to adversarial examples. Various robust decision tree algorithms exist; however, they either do not provide optimal results or are not scalable with data that has continuous features. In this work, we demonstrate RobTree, a scalable optimal robust decision tree algorithm for continuous features. We propose new theorems that reduce the number of thresholds to be considered to half of what was previously considered and give way to pruning techniques. The results of this paper indicate that RobTree vastly outperforms the state-of-the-art in terms of runtime for trees of depth two up to two orders of magnitude.

Deep reinforcement learning has shown strong performance in continuous control tasks, but its reliance on deep neural networks (DNNs) hinders interpretability, limiting deployment in safety-critical domains. While recent approaches using differentiable decision trees improve transparency, they often rely on fixed structures that limit flexibility and lead to unnecessarily complex policies.

We propose SPLIT-PO (Sparse Piecewise-Linear Interpretable Tree Policy Optimization), a novel framework that learns sparse, interpretable decision trees with linear leaf controllers and dynamically adaptive structure. SPLIT-PO introduces learnable gating and regularization to prune uninformative branches during training, enabling compact tree policies to emerge automatically. It maintains end-to-end differentiability and integrates crispification within the training loop, building on prior interpretable methods like ICCT.

Experiments on standard continuous control benchmarks show that SPLIT-PO matches neural network performance (e.g., 285 vs. 287 average reward on Lunar Lander) while producing trees with 100–1000× fewer parameters and as few as 1–3 leaf nodes. Additionally, we prove SPLIT-PO is a universal function approximator, offering neural-level expressivity in an interpretable form. Although it requires more samples to converge, SPLIT-PO provides a promising foundation for transparent and verifiable reinforcement learning.

This research addresses the challenge of interpretability in Reinforcement Learning (RL) for environments with continuous action spaces by extending the Decision Tree Policy Optimization (DTPO) algorithm, which was originally developed for discrete action spaces.
Unlike deep RL methods such as Proximal Policy Optimization (PPO), which are effective but difficult to interpret, DTPO offers transparent rule-based policies. We propose a continuous-action variant of the DTPO algorithm, DTPO-c, which allows decision trees to output Gaussian distribution parameters while maintaining interpretability. Our experiments on the Pendulum-v1 environment show that DTPO-c can achieve performance comparable to Robust Policy Optimization (RPO), although it requires more computational effort. Additionally, we investigate the impact of discretizing continuous actions and find that increasing action resolution does not always lead to improved performance, likely due to limited model capacity. These results confirm the feasibility of interpretable RL in continuous environments, making it suitable for applications where understanding and trusting the behavior of the model is important.

Complex reinforcement learning (RL) models that receive high rewards in their environments are often hard to understand. To this end, more interpretable models can be used, such as decision trees. To be able to deploy these models in safety-critical environments, they need to be high-performing and verifiable. Optimal decision trees can fulfill both these goal. While some methods already exist to find optimal decision trees, none have applied them to RL environments with continuous state
and action spaces [4; 13]. Broccoli is a state-of-the-art approach to synthesizing decision tree policies for blackbox environments [3]. Given a discretisation of the continuous state space, it can find the optimal tree in discrete action environments.
This research will focus on discretising action spaces of continuous environments. In doing so, discrete action spaces are created for which Broccoli can find optimal decision trees. Additionally, a goal is to show that it is possible to discretise continuous action spaces and compute corresponding optimal decision trees in feasible time. Furthermore, it proposes informed discretisation techniques that result in better-performing decision tree policies.

Reinforcement learning models are being utilised in a wide range of industries where even minor mistakes can have severe consequences. For safety reasons, it is important that a human expert can verify the decision-making process of a model. This is where interpretable reinforcement learning proves its importance. This research is focused on training decision tree policies with a limited size and evaluating them on continuous action space environments. For that, a DAGGER algorithm is used with appropriate modifications to account for the continuous setting. The results demonstrate that small decision trees can replicate the high-performing neural network policies (e.g., TD3), achieving close to benchmark scores. Therefore, it is possible to explain the complex model's behaviour with much more understandable structures.

Machine learning models are increasing in popularity and are nowadays used in a wide range of critical applications in fields such as Automotive, Aviation and Medical. Among machine learning models, tree ensemble models are a popular choice due to their competitive performance and high degree of explainability. Like most machine learning models they however suffer from adversarial examples: slightly perturbed input for which the model makes an unexpected prediction. These can be seen as bugs in the model and in critical applications such a bug may have high impact. We investigate if fuzzers, a popular and effective tool for identifying bugs in software, can be used for finding bugs (adversarial examples) in tree ensemble models as well.

We introduce FATE, a tool based on grey-box fuzzers that is able to find adversarial examples on a multitude of datasets. Using a custom mutator that leverages domain information as well as model-specific information such as splitting thresholds and dataset-specific information such as training samples, FATE is able to find good adversarial examples: for non-image classification models they are within 1 percent-point difference from examples generated by the state-of-the-art (Zhang et al., 2020). However, the coverage-guidance of grey-box fuzzers actually limits the performance of FATE: running the mutator of FATE as a (1+1) Evolutionary Algorithm makes FATE show competitive performance to the state-of-the-art, even outperforming it on some datasets.