Tool-Aided Evolutionary LLM for Generative Policy Toward Efficient Resource Management in Wireless Federated Learning

Federated Learning (FL) enables distributed model training across edge devices in a privacy-friendly manner. However, its efficiency heavily depends on effective device selection and high-dimensional resource allocation in dynamic and heterogeneous wireless environments. Conventional methods demand a confluence of domain-specific expertise, extensive hyperparameter tuning, and/or heavy interaction cost. This paper proposes a Tool-aided Evolutionary Large Language Model (T-ELLM) framework to generate a qualified policy for device selection in a wireless FL environment. Unlike conventional optimization methods, T-ELLM leverages natural language-based scenario prompts to enhance generalization across varying network conditions. The framework decouples the joint optimization problem mathematically, enabling tractable learning of device selection policies while delegating resource allocation to convex optimization tools. To improve adaptability, T-ELLM integrates a sample-efficient, model-based virtual learning environment that captures the relationship between device selection and learning performance, facilitating subsequent group relative policy optimization. This concerted approach reduces reliance on real-world interactions, minimizing communication overhead while maintaining high-fidelity decision-making. Theoretical analysis proves that the discrepancy between virtual and real environments is bounded, ensuring the advantage function learned in the virtual environment maintains a provably small deviation from real-world conditions. Experimental results demonstrate that T-ELLM outperforms benchmark methods in energy efficiency and exhibits robust adaptability to environmental changes.