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

TL;DR

The paper addresses designing data recommendations under a target revenue constraint by formulating a KL-divergence minimization problem $\min D(P\|U)$ subject to $R(P)\ge\beta$. It derives that, for feasible revenue, the optimal recommendation distribution $P^*$ takes the form of a normalized message importance measure with a tunable coefficient $\varpi$, unifying advertising and noncommercial regimes into a single framework. Key contributions include explicit optimal solutions for advertising and noncommercial systems, a detailed analysis of monotonicity and geometry of $P^*$, and a demonstrated link between data recommendation and MIM, enabling principled control over attention to high- or low-probability data. The results provide a principled approach to balancing recommendation accuracy and revenue, with practical implications for push-based systems in wireless networks and big-data contexts.

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.

Figures (6)

• Figure 1: System model.
• Figure 2: Probability simplex and optimal recommendation. Region ⓘ denotes Case ⓘ in Table \ref{['tab:result2']} for $1\le i \le 8$.
• Figure 3: $g(\varpi,P)$ vs $\varpi$.
• Figure 4: The optimal recommendation distribution vs minimum average revenue. The parameters set $\{C_p,R_p,C_n,R_{ad},C_m\}$ is denoted by D1 and D2, where D1 $=\{4.5,2,2,11,2\}$ and D2 $=\{1,9,2,3,2\}$. The utility distributions are U1$=\{0.1,0.2,0.3,0.4\}$ and U2$=\{0.05,0.15,0.3,0.5\}$.
• Figure 5: Minimum KL distance between recommendation distribution and utility distribution vs minimum average revenue. The parameters set $\{C_p,R_p,C_n,R_{ad},C_m\}$ is denoted by D1 and D2, where D1 $=\{4.5,2,2,11,2\}$ and D1 $=\{1,9,2,3,2\}$. The utility distribution is U1$=\{0.1,0.2,0.3,0.4\}$ and U2$=\{0.05,0.15,0.3,0.5\}$.

Theorems & Definitions (20)

• Remark 1
• Lemma 1
• proof
• Lemma 2
• proof
• Theorem 1
• proof
• Remark 2
• Theorem 2
• proof