A significant amount of society's infrastructure can be modeled using graph structures, from electric and communication grids, to traffic networks, to social networks. Each of these domains are also susceptible to the cascading spread of negative impacts, whether this be overloaded devices in the power grid or the reach of a social media post containing misinformation. The potential harm of a cascade is compounded when considering a malicious attack by an adversary that is intended to maximize the cascading impact. However, by exploiting knowledge of the cascading dynamics, targets with the largest cascading impact can be preemptively prioritized for defense, and the damage an adversary can inflict can be mitigated. While game theory provides tools for finding an optimal preemptive defense strategy, existing methods struggle to scale to the context of large graph environments because of the combinatorial explosion of possible actions that occurs when the attacker and defender can each choose multiple targets in the graph simultaneously. The proposed method enables a data-driven deep learning approach that uses multi-node representation learning and counterfactual data augmentation to generalize to the full combinatorial action space by training on a variety of small restricted subsets of the action space. We demonstrate through experiments that the proposed method is capable of identifying defense strategies that are less exploitable than SOTA methods for large graphs, while still being able to produce strategies near the Nash equilibrium for small-scale scenarios for which it can be computed. Moreover, the proposed method demonstrates superior prediction accuracy on a validation set of unseen cascades compared to other deep learning approaches.

翻译：社会中大量基础设施可通过图结构建模，从电力与通信网络、交通网络到社交网络。这些领域均容易受到负面影响的级联传播，无论是电网中的过载设备还是社交媒体上传播的错误信息。当考虑恶意攻击者意图最大化级联影响时，级联的潜在危害会进一步加剧。然而，通过利用对级联动力学的知识，可以优先防御具有最大级联影响的目标，从而减轻攻击者可能造成的损害。尽管博弈论提供了寻找最优先发防御策略的工具，现有方法难以扩展到大规模图环境，因为攻击者和防御者均可同时选择图中的多个目标，导致可能动作的组合爆炸。所提方法采用数据驱动的深度学习途径，通过多节点表示学习和反事实数据增强，在多种小规模受限动作子集上训练，从而泛化到完整组合动作空间。实验证明，所提方法能够识别出比现有最先进方法在大规模图上更不易被利用的防御策略，同时在小规模场景中能生成接近纳什均衡的策略（可计算范围内）。此外，与其他深度学习方法相比，所提方法在未见级联的验证集上展现出更优的预测精度。