Deep Reinforcement Learning with Directed Asymmetry and Kolmogorov-Arnold Networks for Dismantling Interdependent Multiplex Networks

Abstract

Identifying the minimum-cost node-removal sequence that fragments a complex network - the network dismantling problem is NP-hard and central to infrastructure resilience. In interdependent multiplex networks, this difficulty is compounded by cascading cross-layer failures. While deep reinforcement learning (DRL) agents utilizing graph neural network (GNN) encoders achieve near-optimal dismantling, current state-of-the-art architectures suffer from two critical limitations. Topologically, existing agents strictly assume undirected edges, rendering them inapplicable to directed systems - such as supply chains or gene regulatory cascades - where failure propagation is fundamentally asymmetric. To resolve this, we propose Disassembling Directed Interdependent Networks (DDIN). DDIN introduces an asymmetric GraphSAGE encoder that explicitly separates incoming influence from outgoing control aggregations, paired with a multi-relational attention mechanism for cross-layer dependency fusion. Evaluated zero-shot on five real-world directed networks, DDIN achieves a 16-23% reduction in the Area Under the Dismantling Curve (AUDC) over heuristic baselines. Functionally, existing GNN encoders parameterise message-passing through multi-layer perceptrons (MLPs). These fixed-affine projections lack the capacity to model the non-smooth, high-frequency vulnerability patterns governing cascading fragility in scale-free topologies. We address this by proposing Kolmogorov-Arnold Reinforcement Learning (KARL), the first architecture to embed learnable univariate functions into an off-policy DRL combinatorial optimiser. KARL features a residual B-spline KAN encoder to stabilise gradient norms during deep message-passing, a fully KAN-parameterised cross-layer attention module (KANformer), and an orthogonal Chebyshev-KAN action-value head to mitigate boundary oscillations under non-stationary temporal-difference targets. Evaluated zero-shot on six real-world undirected multiplex networks, KARL yields a 21.96% average AUDC improvement over state-of-the-art baselines, alongside emergent structural interpretability. By independently resolving the directed topology limitation and the affine expressivity bottleneck, this dissertation establishes a robust architectural foundation for structurally faithful network dismantling models.