Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Mitigating Cascading Effects in Large Adversarial Graph Environments

James D. Cunningham, Conrad S. Tucker

TL;DR

This work tackles the problem of defending large adversarial graphs against cascading failures, where the attacker and defender each select two targets among $\binom{N}{2}$ possibilities, making exact Nash equilibrium computation intractable for large networks. It introduces a data-driven framework that combines Graph Neural Networks with multi-node embeddings, action-space partitioning, and Counterfactual Data Augmentation (CfDA) to learn strategies across the full combinatorial action space. The method supports two generic cascade models—threshold-based and shortest-path—through dedicated counterfactual validations and a payoff-prediction network that outputs per-node failure probabilities. Experiments show near-NE performance on small graphs and reduced exploitability on large graphs, with CfDA providing substantial data efficiency and improved generalization to unseen cascades; these results suggest scalable, expressive defenses in infrastructure-like graph environments. The approach holds practical significance for designing resilient networks by enabling principled, scalable defense planning in the presence of intelligent adversaries.

Abstract

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.

Mitigating Cascading Effects in Large Adversarial Graph Environments

TL;DR

This work tackles the problem of defending large adversarial graphs against cascading failures, where the attacker and defender each select two targets among possibilities, making exact Nash equilibrium computation intractable for large networks. It introduces a data-driven framework that combines Graph Neural Networks with multi-node embeddings, action-space partitioning, and Counterfactual Data Augmentation (CfDA) to learn strategies across the full combinatorial action space. The method supports two generic cascade models—threshold-based and shortest-path—through dedicated counterfactual validations and a payoff-prediction network that outputs per-node failure probabilities. Experiments show near-NE performance on small graphs and reduced exploitability on large graphs, with CfDA providing substantial data efficiency and improved generalization to unseen cascades; these results suggest scalable, expressive defenses in infrastructure-like graph environments. The approach holds practical significance for designing resilient networks by enabling principled, scalable defense planning in the presence of intelligent adversaries.

Abstract

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.
Paper Structure (23 sections, 2 theorems, 12 equations, 7 figures, 5 tables)

This paper contains 23 sections, 2 theorems, 12 equations, 7 figures, 5 tables.

Table of Contents

  1. Introduction
  2. Introduction
  3. Related Work
  4. Graph Feature Extraction
  5. Security of Graph Environments
  6. Models of Cascading Failure
  7. Preliminaries
  8. Security Game Model
  9. Cascading Failure
  10. Threshold-based Cascading Failure
  11. Shortest-Path Cascading Model
  12. Method
  13. Factual Data Generation
  14. Counterfactual Data Generation
  15. Threshold-based Cascading Model
  16. ...and 8 more sections

Key Result

Proposition 1

Given $c(\cdot)$ is the threshold-based model of cascading failure as defined in (eq:threshcasc), the condition (eq:val_criterion) is true if and only if $\phi_v > \frac{|\mathcal{N}(v) \cap \hat{\Omega}|}{|\mathcal{N}(v)|}, \; \forall v \notin \hat{\Omega}$ holds.

Figures (7)

  • Figure 1: Size of payoff matrix for security game with $N$ targets and ${N}\choose{2}$ actions available to both the attacker and defender, plotted in logarithmic scale.
  • Figure 2: An example of a cascade in the threshold-based cascading model. The initial failed node is marked with a red "X", and this failure causes Cascade 1 which is marked with a causal arrow. As a result of Cascade 1, Cascade 2 occurs, and so on with Cascade 3.
  • Figure 3: An example of load redistribution according to shortest-path cascade rules. The red "X" marks the initial failed node, and the dashed lines represent the shortest paths between nodes that traveled through this node before it failed. The solid lines represent the redirected shortest paths after the node failed. The black lines indicate that multiple paths are following the same route. Also indicated is all the nodes that gain load as a result of the initial failure, and how much load is gained.
  • Figure 4: Illustration of the factual data generation process. The full action space with all nodes available to both players is broken down into $p$ subaction spaces with limited sets of nodes available to target (outlined in blue). In each of the $q$ trials, the node choices by the attacker (red) and defender (green) are recorded as well as the nodes that belong to $\Omega$ for the trial (marked with red "X").
  • Figure 5: Illustration of the general counterfactual generation process. A counterfactual action is created by mixing attack and defense actions from two different factual trials that come from different subaction spaces. All failures associated with the attack actions are also incorporated into the counterfactual trial. Then, this counterfactual example is evaluated on its realizability under the specified cascading dynamics and added to the counterfactual dataset if it is feasible.
  • ...and 2 more figures

Theorems & Definitions (4)

  • Proposition 1
  • proof
  • Proposition 2
  • proof