

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

While the input clusters will be disjoint, the base learner may very well generalize its input such that various pairs of plans become comparable in multiple pHTNs within H. Any disagreement is resolved by voting; recall that, given a pHTN H
and a plan p, we can efficiently compute the most probable parse of p by H and its (a priori) likelihood, say ℓH(p). Given two plans p and q we let ≺H order p and q by ℓH(·), i.e., p ≺H q ⇐⇒ ℓH(p) < ℓH(q); if either is not parsable (or tied)
then they are incomparable by H. Given a set of pHTNs H = {H1, H2**, . . .**}, we take a simple majority vote to decide p ≺H q (ties are incomparable):

$$p\prec_{\bf H}q\iff|\{{\cal H}\in{\bf H}\mid q\prec_{\cal H}p\}|<|\{{\cal H}\in{\bf H}\mid p\prec_{\cal H}q\}|.\tag{15}$$

So, each pHTN votes, based on likelihood, for p ≺ q (meaning p is preferred to q), or q ≺ p (q is preferred to p), or abstains (the preference is unknown).

Summarizing, the input Φ is 1) clustered and 2) transitively closed, producing clusters C, 3) each of which is given to the base learner, resulting in a set of pHTNs H modeling the user's preferences via the relation ≺H.

## 4.4. Evaluation

In this part we are primarily interested in evaluating the rescaling extension of the learning technique, i.e., the ability to learn preferences despite feasibility constraints. We design a simple experiment to demonstrate that learning purely from observations is easily confounded by constraints placed in the way of user pref-