A key problem in network theory is how to reconfigure a graph in order to optimize a quantifiable objective. Given the ubiquity of networked systems, such work has broad practical applications in a variety of situations, ranging from drug and material design to telecommunications. The large decision space of possible reconfigurations, however, makes this problem computationally intensive. In this paper, we cast the problem of network rewiring for optimizing a specified structural property as a Markov Decision Process (MDP), in which a decision-maker is given a budget of modifications that are performed sequentially. We then propose a general approach based on the Deep Q-Network (DQN) algorithm and graph neural networks (GNNs) that can efficiently learn strategies for rewiring networks. We then discuss a cybersecurity case study, i.e., an application to the computer network reconfiguration problem for intrusion protection. In a typical scenario, an attacker might have a (partial) map of the system they plan to penetrate; if the network is effectively "scrambled", they would not be able to navigate it since their prior knowledge would become obsolete. This can be viewed as an entropy maximization problem, in which the goal is to increase the surprise of the network. Indeed, entropy acts as a proxy measurement of the difficulty of navigating the network topology. We demonstrate the general ability of the proposed method to obtain better entropy gains than random rewiring on synthetic and real-world graphs while being computationally inexpensive, as well as being able to generalize to larger graphs than those seen during training. Simulations of attack scenarios confirm the effectiveness of the learned rewiring strategies.

翻译：网络理论中的一个关键问题是如何重新配置图结构以优化可量化的目标。鉴于网络系统无处不在，此类研究在从药物与材料设计到电信通信的多种场景中具有广泛的实际应用价值。然而，可能的重新配置方案构成的巨大决策空间使得该问题计算复杂度极高。本文将针对优化特定结构属性的网络重连问题建模为马尔可夫决策过程(MDP)，其中决策者被赋予按序执行的有限修改预算。我们随后提出一种基于深度Q网络(DQN)算法与图神经网络(GNN)的通用方法，该方法可高效学习网络重连策略。进一步地，我们讨论了一个网络安全案例研究，即应用于入侵防护的计算机网络重配置问题。在典型场景中，攻击者可能持有其计划渗透系统的（部分）拓扑图；若网络被有效"打乱"，其先验知识将失效，从而无法导航该网络。这可视作熵最大化问题，其目标在于增强网络的不可预测性。事实上，熵可作为衡量网络拓扑导航难度的代理指标。我们证明所提方法在合成与真实世界图上均能获得比随机重连更优的熵增益，同时保持较低计算开销，并具备向比训练时更大规模图结构泛化的能力。攻击场景的仿真验证了所学重连策略的有效性。