## 4 Discussion
In the case of the experiment described in Section 2.6, we obtained three trees for each parameter setting, examples of which can be seen in Figures 9-11. They approximated the NN decision classifying forward-backward moving, left-right turning, and jumping, respectively. Example decision paths of these trees are shown in Figures 12-14. The decision paths should be analyzed in conjunction with Figure 4, which shows the input image to the NN network. In Figure 12 for both images, the decision to move forward was made. As can be seen, such a decision was made when the Central part of proxy geometry was occupied by an object of class Platform, the South part of the geometry was occupied by an object of class Ground, there was a low number of pixels of Collectible class in the Center, and there were pixels of class Ground in the South-East. In other words, the Agent moved forward if there was Ground under its \"legs\" and a Platform and a Collectible in front of it. In Figure 13, in both cases, the decision was \"Stop\", which means there was no turn in the left or right directions. As can be seen, the decision was based on the statistic that Agents did not turn if both to the left and right of the Agent there were not a sufficiently large number of pixels belonging to the Platform and Collectible classes. Figure 14 shows the situation when the Jump was not made (a) and when the Agent jumped (b). As can be seen, the Jump was not executed because in the South area, there were not enough pixels belonging to the Platform class, and in the South East direction, there were no pixels belonging to the Sky class, but there were pixels of the Ground class. As can be seen in tree (b), the Agent performed the Jump action when there was a Platform object and relatively few pixels of the Ground class in the South area, in the region very close to the Agent. The Agent decided to jump when it moved close enough to the Platform. Plotting CARTs as they are in Figures 12-14 where, in addition, we present histograms of the values of each feature in the training set, visualizes how often a given case occurred in the observed environment. The experiment showed that the rules generated by the CART tree were not only characterized by a high level of accuracy but were relatively easy for humans to interpret and led to intuitive conclusions. We can safely say that the high value of the ACC is the most important indicator that signalizes the successful approximation of a black-box model with its explainable equivalent. The \(\alpha\) and \(t\) parameters of the proposed method has to be tuned experimentally;however, experiments showed that those values should have rather low values. In our experiment, \(t\) did not exceed 2, while \(\alpha\) did not exceed 0.2. That other aspect is the relation between the maximal depth of CART and the possibilities of interpreting and understanding the rules contained in this tree by humans. The process of understanding and interpretation is directly related to the individual abilities of each person to analyze this type of conditional systems, but for sure the deeper the tree, the less understandable it becomes. While dealing with scenarios with multiple actions or decisions, the depth of the decision tree may increase, making rule interpretation more complex. This fact is an inevitable consequence of using a complex decision system in agent control. The more possible actions an agent can take and the more semantic object classes can be distinguished in the environment, the more complex the agent control algorithm and, consequently, the decision tree that describes it usually becomes. To simplify the interpretation process, the tree size can be limited by specifying its maximum depth and the minimum number of samples required to split an internal node. This is a trade-off between the accuracy of the model's description using the decision tree and the complexity of the tree, understood as its depth. A Gini impurity may estimate the overall fitting of the CART on the leaves of a decision tree.