4 minute read

Coppens, Y., Efthymiadis, K., Lenaerts, T., Nowé, A., Miller, T., Weber, R., & Magazzeni, D. (2019, August). Distilling deep reinforcement learning policies in soft decision trees. In Proceedings of the IJCAI 2019 Workshop on Explainable Artificial Intelligence (pp. 1-6).

Paper Summary

This paper presents an XRL technique to explain the global policy of an agent by training a surrogate tree-based model and visualizing its learned weights. A dataset of states and corresponding action distributions is used to train a soft decision tree (SDT) which learns features by which it splits the input down into different branches of the tree, with leaf nodes learning an action distribution. The learned weights are visualized using a heat map, and the action distributions are graphed as aids to analysing the policy. The authors provide some analysis of the policy of an agent trained on the Mario AI benchmark and compare the SDT’s performance to the original agent.


A trained agent is used to produce a dataset of $(s, \pi(s))$ records by exploration in the environment. $\pi(s)$ is the action distribution at state $s$. This dataset is used to train an SDT.

Can an agent which learns a Q-function be used to output this action distribution? It would depend on the action selection mechanism, but I think yes.

An SDT is a hybrid tree-based model which combines binary decision trees with neural networks. A depth is predetermined, which fixes the tree structure. Each node takes as input a state and outputs a probability with which to pass it down to the right child node. It thus learns a hierarchy of filters which assign an input state to a particular leaf node. The leaf nodes learn a softmax distribution over the actions.

The filters are visualized using a heat map. These filters, in addition to graphs of the action distributions at the leaf nodes, aid in analysing the policy.

Experimental Setup

The authors used the Mario AI benchmark as a test environment. They trained the original agent using actor-critic Proximal Policy Optimization (PPO). The policy of this agent was distilled to SDTs of several depths. Average reward per episode was measured for each SDT model and compared to the original PPO agent. Details of both model architectures and training can be found in the paper.

There should be a more concise term for original agent, or the ‘agent for which explanations are being provided’. A term I’ve seen used is explanandum, a Latin word for ‘the phenomenon being explained’. I would like to modify it to indicate that the phenomenon in question is an RL model. A term used in biomimicry is model to denote the ‘thing that is being mimicked’, which communicates this sentiment well. However, model already has a precise meaning in RL literature, so it might not be wise to overload it with this additional meaning.

Results and Analysis

The authors use the heatmap of the SDT filters to deduce that features like ‘what is directly in front of Mario’ are given more importance, while features like the floor are not considered important.

A visualization of an input state overlayed with the node filters on its path, along with a graph of the action distribution of the leaf node and the PPO agent is shown. The authors use it to show why low-reward coins are not given importance by the policy, and high-reward coins are. They also show that the agent has learned to jump on enemies to kill them.

Figure 3 from Coppens et. al. (2019)

The authors also visualize the action distribution of all leaf nodes in different graphs, showing that the agent generally tends to move to the right, since those actions qualitatively have the highest probabilities accorded to them.

The performance graph (in terms of average reward per episode) shows that SDT performance tends to improve with increasing depth, but still remains quite inferior to the PPO agent’s performance.


The authors discuss visualization of the learned filters in non-spatial settings i.e., settings where the input features are not pixels. They note that the explanations are not in a symbolic form which is presumably more human-readable. Rule-based ML techniques could be applied here, and user tests could be conducted to determine the usefulness of the explanations.

They discuss the possibility of fitting an SDT directly on the data i.e., training an SDT-based RL agent in an environment without mimicking an existing RL agent. Given that the SDTs underperformed compared to the model agent, the authors question the resemblance of the learned policy to the model policy and whether any insights drawn would be valid. They discuss improving the performance of the SDT agent. Finally, they discuss adaptively changing the tree depth.


This is a small but neat paper which explains itself and analyses its limitations well. The actual method is not a significant advancement (use an existing distillation technique, use very basic visualization methods), but the otherwise the analysis is done well.

The problem of explaining the policy is reduced to the problem of explaining the learned filters in the SDT, and the action distributions in the leaf nodes. Explaining filter weights is probably being studied extensively in XAI and we should be able to draw on research there to explain these filters in case of non-spatial environments.

The insights about the policy that were drawn didn’t seem novel, and merely confirmed what was already known. If there was a unique characteristic or bug in the model agent that was described and could be explained by the SDT, that would be more convincing.

Additionally, since the filters are features learned by the SDT which mimics the model agent, it is unclear if any explanation of these features is also a valid explanation of how the model agent processes its input. If two very different processes lead to the same conclusion, are the explanations for those processes equivalent? This probably depends on the use case of the explanations.

Lastly, a user evaluation of these explanations, or an additional analysis of a dissimilar domain would have been useful to have.