What is meant by the rank of the scoring function here?

Question

I've been reading the paper Reinforcement Knowledge Graph Reasoning for Explainable Recommendation (by Yikun Xian et al.) lately, and I don't understand a particular section:

Specifically, the scoring function $f((r,e)|u)$ maps any edge $(r,e)$ to a real-valued score conditioned on user $u$. Then, the user-conditional pruned action space of state $s_t$ denoted by $A_t(u)$ is defined as:

$A_t(u) = \{(r,e)| rank(f((r,e)|u))) \leq \alpha ,(r,e) \in A_t\} $

where $\alpha$ is a predefined integer that upper bounds the size of the action space.

Details about the scoring function can be found in the attached paper.

What I don't understand is: What does rank mean, here? Is the thing inside of it a matrix?

It would be great if someone could explain the expression for the user conditional pruned action space in greater detail.

Answer 1

$\text{rank}(f((r,e)|u))$ in $A_t(u)$ means to compute the value of scoring function $f$ for all pairs $(r,e)\in A_t$ which are conditioned by $u$, then sort them in a descending order. The rank of the $f((r,e)|u)$ in this order is equal to $\text{rank}(f((r,e)|u))$. Hence $\text{rank}(f((r,e)|u)) \leqslant \alpha$ means to select the $\alpha$ top most scored pairs.