IPCS: Interior-Point Method based Client Selection for Federated Learning

Large language models (LLMs) excel in many applications, but their centralized training limits access to distributed data and computational resources, hindering scalability. Federated learning (FL) offers a promising solution by enabling collaborative training. In practical large-scale implementations, federated learning typically adopts a multitiered architecture rather than a conventional flat structure. This hierarchical approach incorporates multiple layers of edge servers that mediate between the cloud server and end devices, forming the multi-level federated learning. However, optimizing client and server selection in such complex systems remains a critical challenge. Traditional Multi-armed Bandit (MAB)based client selection methods yield suboptimal local choices in multi-level FL systems due to their inability to account for global constraints imposed by neighboring nodes. To overcome this limitation, we introduce Interior-Point Method based Client Selection (IPCS), a novel approach that leverages Interior-point Policy Convex Optimization (IPO) to enhance client and server selection in real-world multi-level federated learning. Unlike MAB-based methods, IPCS transforms the selection objective into a logarithmic barrier function, enabling it to efficiently identify the global optimum under complex hierarchical constraints. Our experiments demonstrate that IPCS significantly outperforms MAB-based methods and another state-of-the-art baseline, achieving higher model accuracy, faster convergence, and lower communication costs. These results highlight the effectiveness of IPCS in optimizing largescale, multi-level federated learning systems, paving the way for more scalable and efficient LLM training frameworks.