  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.
