# Matching Users' Preference Under Target Revenue Constraints in Optimal Data Recommendation Systems

## TL;DR

This paper introduces a framework for data recommendation systems that balances user preferences and revenue constraints by utilizing a distribution based on message importance measure (MIM), adaptable to various system needs.

## Contribution

It formulates the recommendation problem as an optimization using relative entropy and connects the optimal solution to the MIM, providing a new theoretical foundation for recommendation strategies.

## Key findings

- Optimal recommendation distribution aligns with normalized MIM.
- Adjusting the importance coefficient tailors recommendations to system requirements.
- The framework validates MIM's physical meaning and rationality in data recommendation.

## Abstract

This paper focuses on the problem of finding a particular data recommendation strategy based on the user preferences and a system expected revenue. To this end, we formulate this problem as an optimization by designing the recommendation mechanism as close to the user behavior as possible with a certain revenue constraint. In fact, the optimal recommendation distribution is the one that is the closest to the utility distribution in the sense of relative entropy and satisfies expected revenue. We show that the optimal recommendation distribution follows the same form as the message importance measure (MIM) if the target revenue is reasonable, i.e., neither too small nor too large. Therefore, the optimal recommendation distribution can be regarded as the normalized MIM, where the parameter, called importance coefficient, presents the concern of the system and switches the attention of the system over data sets with different occurring probability. By adjusting the importance coefficient, our MIM based framework of data recommendation can then be applied to system with various system requirements and data distributions.Therefore,the obtained results illustrate the physical meaning of MIM from the data recommendation perspective and validate the rationality of MIM in one aspect.