# Iterative Oblique Decision Trees Deliver Explainable RL Models
## 5 Discussion  
For a broader perspective, we want to point out a number of issues related to our findings. 1. To align our work in the context of XAI, we may use the guidance of the taxonomy proposed by ([PERSON] and [PERSON] (2018), Section 5): * The **problem definition**: The **task** consists of a classification or regression (for discrete or continuous actions, respectively) of tabular, numerical data (observations). We intend a **post hoc** explanation of DRL oracles, by finding **decision trees** described that are inherently transparent and simulatable in that a human can follow the simple mathematical and hierarchical structure of a DT's decision-making process. * Our algorithm as an **explanator** requires a model (the oracle and also the environment's dynamics) as **input**, while still being portable by not relying on a specific type of oracle. The **output** data of our algorithm are shallow DTs as surrogate models mimicking the decision-making process of the DRL oracles. This leads to a drastic reduction of model parameters (see Table 4). Given their simple and transparent nature, DTs lend themselves to rule-based output and to further explanations by example or by counterfactuals, and analysis of feature importance (as we showed in Section 4.4.3). * As the fundamental **functionally grounded metric** of our algorithm, we compare the DT's average return in the RL environment with the oracle's performance. This measures the fidelity to the oracle in the regions relevant to successfully solve the environment and the accuracy with respect to the original task of the environment. We do not evaluate **human-grounded** metrics. (Human-grounded metrics are defined by [PERSON] and [PERSON] (2018) as metrics involving human judgment of the explainability of the constructed explanator (here: DT): how easy is it for humans to build a mental model of the DT, how accurately does the mental model approximate the explanator model, and so on.) Instead, we trust that the simple structure and mathematical expressions used in the DTs generated by our algorithms, as well as the massively reduced number of model parameters, lead to an interpretability and effectiveness of predictions that could not be achieved with DRL models. In Section 4.4, we have explained aspects connected to this in more detail. 2. Can we understand _why_ the combination ITER + OPCT is successful, while the combination EPS + OPCT is not? We have no direct proof, but from the experiments conducted, we can share these insights: Firstly, equilibrium problems such as Cart-Pole or Pendulum exhibit a severe oversampling of some states (i.e., the upright pendulum state). If, as a consequence, the initial DT is not well-performing, ITER allows to add the correct oracle actions for problematic samples and to improve the tree in critical regions of the observation space. Secondly, for environment Pendulum we observed that the initial DT was \"bad\" because it learned only from near-perfect oracle episodes. It had not seen any samples outside the near-perfect episode region and hypothesized the wrong actions in the _outside_ regions (see Figure 3). Again, ITER helps; a \"bad\" DT is likely to visit these _outside_ regions and then add samples combined with the correct oracle actions to its sample set. We conclude that algorithm ITER is successful because it strikes the right balance between being too exploratory, like algorithm BB (which might sample from constraint-violating regions or from regions unknown to the oracle), and not exploratory enough, like algorithm EPS (which might sample only from the narrow region of successful oracle trajectories). Algorithm ITER solves the sampling challenges mentioned in Section 1. It works well based on its iterative nature, which results in self-correction of the tree. At every iteration, the trajectories generated by the tree form a dataset of state-action pairs. The oracle corrects the wrong actions, and the tree can improve its behavior based on the enlarged dataset. 3.