通过分层LoRA分解，实现多模态大模型的高效个性化联邦学习。

Agentic AI systems are reshaping communications and networking by deploying autonomous intelligent agents capable of collaborative learning while maintaining data privacy at network edges. Within distributed network environments, Multimodal Large Language Models (MLLMs) serve as cognitive engines for edge devices, yet federated fine-tuning faces substantial challenges in balancing global knowledge aggregation with local adaptation under heterogeneous network conditions. Conventional federated protocols typically rely on uniform parameter aggregation, which conflates domain-invariant features with client-specific nuances, thereby resulting in suboptimal personalization and excessive communication overhead. To address these challenges, we propose PFAdapter, a communication-efficient framework introducing hierarchical LoRA decomposition to explicitly separate adapter parameters into global-shared and local-private components. Query and key projections are assigned to global synchronization for capturing universal multimodal semantics across the network, while value and output projections remain localized for edge-specific adaptation. Additionally, orthogonality regularization based on the Frobenius norm enforces strict separation between these components, preventing redundant feature learning. Selective aggregation protocols synchronize only global-shared components across the federated network, preserving local expertise and reducing communication costs by nearly 50%. Extensive experiments on VQA-RAD, SLAKE, Hateful Memes, and CrisisMMD datasets demonstrate that PFAdapter consistently outperforms state-of-the-art baselines, achieving accuracy improvements ranging from 2.4% to 4.8% across diverse edge intelligence tasks. Consequently, our framework establishes an efficient solution for agentic AI deployment in resource-constrained communication networks.