# ToupleGDD: A Fine-Designed Solution of Influence Maximization by Deep Reinforcement Learning

arXiv: https://arxiv.org/abs/2210.07500 · HTML: https://mlsanity.com/paper/2210.07500/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 44 references that are in the map.
- First posted on arXiv 14 Oct 2022.

## Builds on (most cited first, 15 of 15)

- [Deep Reinforcement Learning with Double Q-learning](https://mlsanity.com/paper/1509.06461/) (2015)
- [Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/1812.08434/) (2018)
- [Machine Learning for Combinatorial Optimization: a Methodological Tour d'Horizon](https://mlsanity.com/paper/1811.06128/) (2018)
- [Learning Combinatorial Optimization Algorithms over Graphs](https://mlsanity.com/paper/1704.01665/) (2017)
- [Reinforcement Learning for Combinatorial Optimization: A Survey](https://mlsanity.com/paper/2003.03600/) (2020)
- [Combinatorial Optimization with Graph Convolutional Networks and Guided Tree Search](https://mlsanity.com/paper/1810.10659/) (2018)
- [Discriminative Embeddings of Latent Variable Models for Structured Data](https://mlsanity.com/paper/1603.05629/) (2016)
- [Influence Maximization: Near-Optimal Time Complexity Meets Practical Efficiency](https://mlsanity.com/paper/1404.0900/) (2014)
- [Popularity Prediction on Social Platforms with Coupled Graph Neural Networks](https://mlsanity.com/paper/1906.09032/) (2019)
- [Influence maximization in unknown social networks: Learning Policies for Effective Graph Sampling](https://mlsanity.com/paper/1907.11625/) (2019)
- [Stop-and-Stare: Optimal Sampling Algorithms for Viral Marketing in Billion-scale Networks](https://mlsanity.com/paper/1605.07990/) (2016)
- [Contingency-Aware Influence Maximization: A Reinforcement Learning Approach](https://mlsanity.com/paper/2106.07039/) (2021)
- [DISCO: Influence Maximization Meets Network Embedding and Deep Learning](https://mlsanity.com/paper/1906.07378/) (2019)
- [A Survey on Reinforcement Learning for Combinatorial Optimization](https://mlsanity.com/paper/2008.12248/) (2020)
- [LeNSE: Learning To Navigate Subgraph Embeddings for Large-Scale Combinatorial Optimisation](https://mlsanity.com/paper/2205.10106/) (2022)

## Built on by (most cited first, 11 of 11)

- [Deep Graph Representation Learning and Optimization for Influence Maximization](https://mlsanity.com/paper/2305.02200/) (2023)
- [A Survey on Influence Maximization: From an ML-Based Combinatorial Optimization](https://mlsanity.com/paper/2211.03074/) (2022)
- [Critical Nodes Identification in Complex Networks: A Survey](https://mlsanity.com/paper/2507.06164/) (2025)
- [MIM-Reasoner: Learning with Theoretical Guarantees for Multiplex Influence Maximization](https://mlsanity.com/paper/2402.16898/) (2024)
- [Non-Progressive Influence Maximization in Dynamic Social Networks](https://mlsanity.com/paper/2412.07402/) (2024)
- [Influence Strength Estimation in Hyperbolic Space for Social Influence Maximization](https://mlsanity.com/paper/2502.13571/) (2025)
- [Vulnerable Agent Identification in Large-Scale Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2509.15103/) (2025)
- [Scale-Adaptive Power Flow Analysis with Local Topology Slicing and Multi-Task Graph Learning](https://mlsanity.com/paper/2601.01387/) (2026)
- [SP-GCRL: Influence Maximization on Incomplete Social Graphs](https://mlsanity.com/paper/2605.12513/) (2026)
- [Placing Degree Scales After LayerNorm](https://mlsanity.com/paper/2606.14022/) (2026)
- [Rethinking Learning-Based Influence Maximization: Simple Neural Surrogates and Native Discrete Search](https://mlsanity.com/paper/2608.08406/) (2026)

## Abstract (arXiv)

Aiming at selecting a small subset of nodes with maximum influence on networks, the Influence Maximization (IM) problem has been extensively studied. Since it is #P-hard to compute the influence spread given a seed set, the state-of-the-art methods, including heuristic and approximation algorithms, faced with great difficulties such as theoretical guarantee, time efficiency, generalization, etc. This makes it unable to adapt to large-scale networks and more complex applications. On the other side, with the latest achievements of Deep Reinforcement Learning (DRL) in artificial intelligence and other fields, lots of works have been focused on exploiting DRL to solve combinatorial optimization problems. Inspired by this, we propose a novel end-to-end DRL framework, ToupleGDD, to address the IM problem in this paper, which incorporates three coupled graph neural networks for network embedding and double deep Q-networks for parameters learning. Previous efforts to solve IM problem with DRL trained their models on subgraphs of the whole network, and then tested on the whole graph, which makes the performance of their models unstable among different networks. However, our model is trained on several small randomly generated graphs with a small budget, and tested on completely different networks under various large budgets, which can obtain results very close to IMM and better results than OPIM-C on several datasets, and shows strong generalization ability. Finally, we conduct a large number of experiments on synthetic and realistic datasets, and experimental results prove the effectiveness and superiority of our model.