Reinforcement learning (RL) has shown promise for combinatorial optimization problems on graphs by learning heuristics that generalize across instances. However, effectively incorporating domain knowledge into RL frameworks for graph partitioning remains challenging, as existing approaches typically rely on unconstrained node-level actions that lead to large action spaces and inefficient exploration. In this paper, we propose RidgeCut, an RL framework that constrains the action space to enforce structure-aware partitioning in the Normalized Cut problem. Using transportation networks as a motivating example, we introduce a novel concept that leverages domain knowledge about urban road topology -- where natural partitions often take the form of concentric rings and radial wedges. By transforming the graph into linear or circular representations, our method enables the use of transformer-based policies and efficient learning via Proximal Policy Optimization. The resulting partitions from RidgeCut are not only aligned with expected spatial layouts but also achieve lower normalized cuts compared to existing methods. Experimental results on synthetic and real-world traffic graphs demonstrate that RidgeCut consistently outperforms existing methods while exhibiting strong inductive generalization across graph sizes. Although motivated by road networks, RidgeCut provides a general mechanism for embedding structural priors into RL frameworks for graph partitioning.

翻译：强化学习（RL）通过学习跨实例泛化的启发式策略，在解决图上的组合优化问题中展现出潜力。然而，如何有效地将领域知识融入面向图分割的强化学习框架仍然具有挑战性，现有方法通常依赖无约束的节点级动作，导致动作空间过大且探索效率低下。本文提出RidgeCut，一种在归一化割问题中约束动作空间以实现结构感知分割的强化学习框架。以交通网络为典型案例，我们引入了利用城市道路拓扑领域知识（其中自然分割常表现为同心环与放射楔形式）的新颖概念。通过将图转换为线性或环形表征，该方法能够采用基于Transformer的策略，并借助近端策略优化实现高效学习。RidgeCut产生的分割不仅符合预期的空间布局，且相较于现有方法实现了更低的归一化割值。在合成图和真实交通图上的实验表明，RidgeCut始终优于现有方法，并在不同图规模间展现出强大的归纳泛化能力。尽管以道路网络为启发，RidgeCut为将结构先验嵌入面向图分割的强化学习框架提供了一种通用机制。