Value at Adversarial Risk: A Graph Defense Strategy against Cost-Aware Attacks

Deep learning methods on graph data have achieved remarkable efficacy across a variety of real-world applications, such as social network analysis and transaction risk detection. Nevertheless, recent studies have illuminated a concerning fact: even the most expressive Graph Neural Networks (GNNs) are vulnerable to graph adversarial attacks. While several methods have been proposed to enhance the robustness of GNN models against adversarial attacks, few have focused on a simple yet realistic approach: valuing the adversarial risks and focused safeguards at the node level. This empowers defenders to allocate heightened security level to vulnerable nodes, while lower to robust nodes. With this new perspective, we propose a novel graph defense strategy RisKeeper, such that the adversarial risk can be directly kept in the input graph. We start at valuing the adversarial risk, by introducing a cost-aware gradient-based graph adversarial attack that takes into account not only cost avoidance and compliance with cost budgets but also addresses the challenges posed by discrete graph data. Subsequently, we present a learnable approach to ascertain the ideal security level for each individual node by solving a bi-level optimization problem. Through extensive experiments on four realworld datasets, we demonstrate that our method achieves superior performance surpassing state-of-the-art methods. Our in-depth case studies provide further insights into vulnerable and robust structural patterns, serving as inspiration for practitioners to exercise heightened vigilance.