Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

MIM-Reasoner: Learning with Theoretical Guarantees for Multiplex Influence Maximization

Nguyen Do, Tanmoy Chowdhury, Chen Ling, Liang Zhao, My T. Thai

TL;DR

This paper introduces MIM-Reasoner, coupling reinforcement learning with probabilistic graphical model, which effectively captures the complex propagation process within and between layers of a given multiplex network, thereby tackling the most challenging problem in MIM.

Abstract

Multiplex influence maximization (MIM) asks us to identify a set of seed users such as to maximize the expected number of influenced users in a multiplex network. MIM has been one of central research topics, especially in nowadays social networking landscape where users participate in multiple online social networks (OSNs) and their influences can propagate among several OSNs simultaneously. Although there exist a couple combinatorial algorithms to MIM, learning-based solutions have been desired due to its generalization ability to heterogeneous networks and their diversified propagation characteristics. In this paper, we introduce MIM-Reasoner, coupling reinforcement learning with probabilistic graphical model, which effectively captures the complex propagation process within and between layers of a given multiplex network, thereby tackling the most challenging problem in MIM. We establish a theoretical guarantee for MIM-Reasoner as well as conduct extensive analyses on both synthetic and real-world datasets to validate our MIM-Reasoner's performance.

MIM-Reasoner: Learning with Theoretical Guarantees for Multiplex Influence Maximization

TL;DR

This paper introduces MIM-Reasoner, coupling reinforcement learning with probabilistic graphical model, which effectively captures the complex propagation process within and between layers of a given multiplex network, thereby tackling the most challenging problem in MIM.

Abstract

Multiplex influence maximization (MIM) asks us to identify a set of seed users such as to maximize the expected number of influenced users in a multiplex network. MIM has been one of central research topics, especially in nowadays social networking landscape where users participate in multiple online social networks (OSNs) and their influences can propagate among several OSNs simultaneously. Although there exist a couple combinatorial algorithms to MIM, learning-based solutions have been desired due to its generalization ability to heterogeneous networks and their diversified propagation characteristics. In this paper, we introduce MIM-Reasoner, coupling reinforcement learning with probabilistic graphical model, which effectively captures the complex propagation process within and between layers of a given multiplex network, thereby tackling the most challenging problem in MIM. We establish a theoretical guarantee for MIM-Reasoner as well as conduct extensive analyses on both synthetic and real-world datasets to validate our MIM-Reasoner's performance.
Paper Structure (14 sections, 7 theorems, 36 equations, 3 figures, 3 tables, 4 algorithms)

This paper contains 14 sections, 7 theorems, 36 equations, 3 figures, 3 tables, 4 algorithms.

Table of Contents

  1. INTRODUCTION
  2. PROBLEM STATEMENT AND BACKGROUND
  3. RELATED WORK
  4. MIM-REASONER
  5. Phase 1. Budget Allocation
  6. Phase 2. Relation RL Optimization
  7. Reinforcement Learning Framework
  8. MIM-Reasoner Analysis
  9. EXPERIMENT EVALUATION
  10. Experiment Setup
  11. Training Time Analysis
  12. Inference Time Analysis
  13. Quantitative Analysis
  14. CONCLUSION

Key Result

Lemma 1

(Greedy Policy Guarantee). When policy $\pi$ is converged, $\pi^*(v \mid S_{i,t})$ always selects nodes greedily at every time step $t$. (Proof in Appendix B.2)

Figures (3)

  • Figure 1: An example of the propagation process in a multiplex network consisting of 2 layers. Layers $G_1$ and $G_2$ operate LT and IC model, respectively. Each node in $G_1$ has a threshold $\zeta \in [0,1]$. The green bold arrow in $G_2$ indicates high probability of activation.
  • Figure 2: MIM-Reasoner consists of two phases: Budget Allocation and Relation RL Optimization. In Phase 1, algorithm $\mathcal{A}$ calculates the profit and cost for each layer in parallel. The 'Multiple Choice Knapsack Problem' is then solved to determine the allocated budget for each layer, presented in the 'Budget Allocation Table'. In Phase 2, an RL-Agent is trained to sequentially find solutions for each layer using the allocated budget. Simultaneously, the status dataset is processed through 'Structure Learning' to create a 'Probabilistic Graphical Model' which reveals layer relationships and helps the RL-Agent to avoid reactivating nodes already activated by other layers.
  • Figure 3: Comparison of five methods on a synthetic dataset, with different overlapping percentages and layers. The comparison is based on two metrics: total spreading and running time (in seconds).

Theorems & Definitions (7)

  • Lemma 1
  • Lemma 2
  • Theorem 1
  • Theorem 2
  • Theorem 3
  • Lemma 3
  • Theorem 4