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.