RLMiner: Finding the Most Frequent k-sized Subgraph via Reinforcement Learning

TL;DR

RLMiner addresses the NP-hard problem of finding the most frequent induced subgraph of size $k$ in a single labeled graph by formulating it as a multi-task reinforcement learning problem and solving it with a task-state-aware Graph Neural Network integrated with Soft Actor-Critic. The approach avoids exhaustive subgraph enumeration during inference and achieves time complexity linear in $k$, while delivering subgraphs with frequencies close to the ground truth on real-world graphs. Key contributions include the task-state-aware GNN, a carefully designed reward scheme that stabilizes training, and evidence that RLMiner outperforms exact enumeration in runtime by orders of magnitude while maintaining high approximation quality. This framework broadens the practicality of frequent subgraph mining in domains like web data and social networks by mitigating combinatorial explosion without relying on Downward Closure-based pruning.

Abstract

Identifying the most frequent induced subgraph of size $k$ in a target graph is a fundamental graph mining problem with direct implications for Web-related data mining and social network analysis. Despite its importance, finding the most frequent induced subgraph remains computationally expensive due to the NP-hard nature of the subgraph counting task. Traditional exact enumeration algorithms often suffer from high time complexity, especially for a large graph size $k$. To mitigate this, existing approaches often utilize frequency measurement with the Downward Closure Property to reduce the search space, imposing additional constraints on the task. In this paper, we first formulate this task as a Markov Decision Process and approach it using a multi-task reinforcement learning framework. Specifically, we introduce RLMiner, a novel framework that integrates reinforcement learning with our proposed task-state-aware Graph Neural Network to find the most frequent induced subgraph of size $k$ with a time complexity linear to $k$. Extensive experiments on real-world datasets demonstrate that our proposed RLMiner effectively identifies subgraphs with frequencies closely matching the ground-truth most frequent induced subgraphs, while achieving significantly shorter and more stable running times compared to traditional methods.

Figures (9)

• Figure 1: An example of frequent subgraph mining. (a) A target graph. (b) and (c) Induced subgraphs of the target graph.
• Figure 2: An overview of RLMiner inference process. In each time step, $RLMiner$ computes the action probability distribution using the Actor network, then select the action with highest probability according to greedy policy.
• Figure 3: Architecture of the Actor network and the Critic network. (a) An overview of the proposed Task-state-aware GNN. (b) An overview of the Actor network prediction head. (c) An overview of the Critic network prediction head.
• Figure 4: Approximation ratio of RLMiner on unseen test target graphs during training for different reward settings.
• Figure 5: Approximation ratio of RLminer on training target graphs during training.