A hierarchical evolutionary deep reinforcement learning algorithm for influence maximization in multilayer hypergraphs

Abstract

Multilayer hypergraphs provide a unified representation of influence diffusion in complex networks by coupling relation layers through shared entities and encoding higher-order group interactions as hyperedges. Existing influence maximization (IM) methods have been extensively studied on ordinary graphs and single-layer hypergraphs, yet they leave two structural limitations unresolved. Single-layer methods cannot represent the propagation of an entity across multiple relation semantics, whereas most multilayer methods still use pairwise edges as their basic diffusion units and therefore omit hyperedge-induced group interactions. We address seed selection under the joint effects of multilayer coupling and higher-order influence by introducing Multi-Layer Hypergraph Linear Threshold with Cross-layer Thresholding (MLH-LT-CT). The model combines a dual-threshold intralayer mechanism for hyperedges and nodes with a δ -threshold rule that couples entity states across relation layers. We extend the non-submodularity result for the single-layer hypergraph linear threshold (LT) model to the multilayer setting and show that cross-layer thresholding can further modify the marginal-gain structure induced by intralayer higher-order coordination. Consequently, the classical ( 1 − 1 / e ) guarantee for submodular greedy maximization does not directly apply. To optimize this non-submodular objective, we propose Hierarchical Influence Via Evolution (HIVE), which integrates population-level global search by differential evolution, adaptive seed-selection guidance from a deep Q-network, and topology-guided local refinement. We also establish an incremental-propagation equivalence theorem from the extensivity, idempotence, and monotonicity of the propagation closure. The theorem establishes equality of the final diffusion state obtained by incremental updates and full recomputation; it is not itself a running-time guarantee. Across 11 synthetic and real multilayer hypergraph datasets, HIVE strictly outperformed MA-IM on eight datasets. The ablation and sensitivity analyses further assess the contributions of evolutionary search, reinforcement-learning guidance, and topology-guided refinement; additional threshold scans characterize the transition between saturated, discriminative, and propagation-suppressed regimes; the correctness of incremental state reuse is established theoretically. These results support explicit cross-layer threshold modeling and hierarchical optimization as a coherent approach to non-submodular influence maximization in multilayer higher-order diffusion systems.