Which reward function works for recommendation systems using knowledge graphs? I've been reading this paper on recommendation systems using reinforcement learning (RL) and knowledge graphs (KGs).

To give some background, the graph has several (finitely many) entities, of which some are user entities and others are item entities. The goal is to recommend items to users, i.e. to find a recommendation set of items for every user such that the user and the corresponding items are connected by one reasoning path.

I'm attaching an example of such a graph for more clarity (from the paper itself) -



In the paper above, they say


  First, we do not have pre-defined targeted items for any user, so it is not applicable to use a binary reward indicating whether the user interacts with the item or not. A better design of the reward function is to incorporate the uncertainty of how an item is relevant to a user based on the rich heterogeneous information given by the knowledge graph.


I'm not able to understand the above extract, which talks about the reward function to use - binary, or something else. A detailed explanation of what the author is trying to convey in the above extract would really help.
I found the answer further into the paper! I'll post it here for everyone.

Given any user, there is no pre-known targeted item in the KGRE-Rec (Knowledge Graph Reasoning for Explainable Recommendation) problem, so it is unfeasible to consider binary rewards indicating whether the agent has reached a target or not.

Instead, the agent is encouraged to explore as many “good” paths
as possible. In the context of recommendations, a “good” path is one that leads to an item that a user will interact with, with high probability. To this end, a soft reward is given only for the terminal state $s_T = (u,e_T,h_T)$ based on a scoring function $f(u,i)$. The terminal reward $R_T$ is given as - 


where the value of $R_T$ is normalized to the range $[0,1]$. Details about $f(u,i)$, the scoring function, can be found in the paper.

References:


Reinforcement Knowledge Graph Reasoning for Explainable
Recommendation [Yikun Xian, Zuohui Fu, S. Muthukrishnan, Gerard
de Melo, Yongfeng Zhang]