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REM: A Scalable Reinforced Multi-Expert Framework for Multiplex Influence Maximization

Huyen Nguyen, Hieu Dam, Nguyen Do, Cong Tran, Cuong Pham

TL;DR

REM tackles Multiplex Influence Maximization by combining a Variational Autoencoder–based Seed2Vec with a Propagation Mixture of Experts to capture diverse diffusion dynamics across multiplex layers. It uses reinforcement-learning–inspired latent exploration to generate seed sets and a priority-replay mechanism to iteratively improve the latent model. Empirical results on five real multiplex networks under IC and LT show REM achieves higher influence spread and faster inference than state-of-the-art baselines, with near-linear scalability. This framework enables robust, scalable seed selection in complex multiplex environments where diffusion patterns are heterogeneous and unknown.

Abstract

In social online platforms, identifying influential seed users to maximize influence spread is a crucial as it can greatly diminish the cost and efforts required for information dissemination. While effective, traditional methods for Multiplex Influence Maximization (MIM) have reached their performance limits, prompting the emergence of learning-based approaches. These novel methods aim for better generalization and scalability for more sizable graphs but face significant challenges, such as (1) inability to handle unknown diffusion patterns and (2) reliance on high-quality training samples. To address these issues, we propose the Reinforced Expert Maximization framework (REM). REM leverages a Propagation Mixture of Experts technique to encode dynamic propagation of large multiplex networks effectively in order to generate enhanced influence propagation. Noticeably, REM treats a generative model as a policy to autonomously generate different seed sets and learn how to improve them from a Reinforcement Learning perspective. Extensive experiments on several real-world datasets demonstrate that REM surpasses state-of-the-art methods in terms of influence spread, scalability, and inference time in influence maximization tasks.

REM: A Scalable Reinforced Multi-Expert Framework for Multiplex Influence Maximization

TL;DR

REM tackles Multiplex Influence Maximization by combining a Variational Autoencoder–based Seed2Vec with a Propagation Mixture of Experts to capture diverse diffusion dynamics across multiplex layers. It uses reinforcement-learning–inspired latent exploration to generate seed sets and a priority-replay mechanism to iteratively improve the latent model. Empirical results on five real multiplex networks under IC and LT show REM achieves higher influence spread and faster inference than state-of-the-art baselines, with near-linear scalability. This framework enables robust, scalable seed selection in complex multiplex environments where diffusion patterns are heterogeneous and unknown.

Abstract

In social online platforms, identifying influential seed users to maximize influence spread is a crucial as it can greatly diminish the cost and efforts required for information dissemination. While effective, traditional methods for Multiplex Influence Maximization (MIM) have reached their performance limits, prompting the emergence of learning-based approaches. These novel methods aim for better generalization and scalability for more sizable graphs but face significant challenges, such as (1) inability to handle unknown diffusion patterns and (2) reliance on high-quality training samples. To address these issues, we propose the Reinforced Expert Maximization framework (REM). REM leverages a Propagation Mixture of Experts technique to encode dynamic propagation of large multiplex networks effectively in order to generate enhanced influence propagation. Noticeably, REM treats a generative model as a policy to autonomously generate different seed sets and learn how to improve them from a Reinforcement Learning perspective. Extensive experiments on several real-world datasets demonstrate that REM surpasses state-of-the-art methods in terms of influence spread, scalability, and inference time in influence maximization tasks.
Paper Structure (23 sections, 3 theorems, 22 equations, 3 figures, 7 tables, 2 algorithms)

This paper contains 23 sections, 3 theorems, 22 equations, 3 figures, 7 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. Problem Formulation
  4. Our Framework: REM
  5. Seed2Vec: Learning To Embed Complex Seed Set
  6. Propagation Mixture of Expert
  7. Latent Seed Set Exploration
  8. Experiment
  9. Experiment Setup
  10. Comparison to other Methods
  11. Quantitative Analysis
  12. Scalability Analysis
  13. Conclusion
  14. A. Detail Steps of REM
  15. B. Detail ELBO
  16. ...and 8 more sections

Key Result

Lemma 1

Assuming the PMoE model has been trained to convergence and during the inference phase, noisy scores $\xi_n$ are not considered, for any GNN-based, $\mathcal{P}$ is infection monotonic if the aggregation function and combine function in GNN are non-decreasing. (Proof in Appendix C1)

Figures (3)

  • Figure 1: An example illustrating the unique "overlapping activation" property of influence propagation in a multiplex network. Two layers $G_1$ and $G_2$ has their own respective diffusion model, LT and IC. Orange nodes represent seed nodes, pink nodes are infected, and green nodes are nodes that are activated due to overlap. If propagation occurs independently within each layer, node $v_6$ of $G_1$ is inactive due to its high threshold of $0.7$, meaning it requires at least $70\%$ activated neighbors to become activated. However, in the multiplex, overlapping node $v_5$ of $G_1$ is also activated due to deterministic activation from $G_2$, meeting activation requirement of node $v_6$ in $G_1$. Therefore, total infected node set of the multiplex, not counting the same node in different layer, is now ($v_2$, $v_4$, $v_5$, $v_6$, $v_8$).
  • Figure 2: The diagram depicts REM's process for addressing the MIM problem. Initially, REM utilizes Seed2Vec to embed complex representations of seed sets into a continuous and less noisy space. Subsequently, REM explores and generates various diverse seed sets from this latent space. REM maintains control over the quality of seed set generation through the Propagation Mixture of Experts (PMoE), a model capable of accurately learning and predicting the propagation of a given seed set in a large-scale multiplex network. Once the synthetic sets are generated, they are stored in a priority replay memory. To prevent model collapse or catastrophic forgetting, the top $k$ seed sets, which PMoE predicts to contribute the most to propagation in multiplex networks, are then combined with the original collected dataset to construct a new dataset for model retraining. This process reinforces the capability to produce higher-quality seed sets in future iterations.
  • Figure 3: Difference in influence spread (y-axis) of REM output on different dataset and budget when increasing exploration steps(x axis). Fig. \ref{['fig: coraml_ic']} - \ref{['fig: paris_attack2015_ic']} and Fig. \ref{['fig: coraml_lt']} - \ref{['fig: paris_attack2015_lt']} are evaluated under the IC and LT model, respectively.

Theorems & Definitions (8)

  • Definition 1: Influence Spread
  • Definition 2: Multiplex Influence Maximization (MIM)
  • Lemma 1: Monotonicity of PMoE Models
  • Lemma 2: Latent Entropy Maximization Equivalence
  • Theorem 3: Influence Estimation Consistency
  • proof
  • proof
  • proof