

![0_image_0.png](0_image_0.png)

measure of conciseness, the one we employ, is the ratio of non-primitives in the learned model to non-primitives in the oracle (n) - the learner is not told how many symbols were used to generate the training data. Figure 3(b) plots results.

For small domains (around n = 10) the learner uses between 10 and 20% more non-primitives, a fairly positive result. However, for larger domains this result degrades to 60% more non-primitives, a somewhat negative result. Albeit the divergence measure improves - on the hidden test set - so while there is some evidence of possible overfitting the result is not alarming. Future work in structure learning should nonetheless examine this issue (conciseness and overfitting)
in greater depth.

Note: Divergence in the recursive case is consistently larger than in the nonrecursive case across all experiments: this is expected. In the recursive case the plan space is actually infinite; in the non-recursive case there are only finitely many plans that can be generated. So, for example, in the non-recursive case, it is actually possible for a finite sample set to perfectly represent the true distribution (simply memorizing the training data will produce 0 divergence eventually).

## 3.5. Benchmark Domains

In addition to the experiments with synthetic domains, we also picked two of the well known benchmark planning domains and simulated possible users (in the form of hand-constructed pHTNs). Logistics Planning: The domain we used in the first experiment is a variant of