Lyapunov-DLD-Based Latency and Power Optimization in 5G O-RAN for Federated Learning

Federated Learning (FL) in 5G Open Radio Access Networks (O-RAN) faces critical challenges such as latency, dynamic power allocation, channel variability, and data heterogeneity, all of which degrade system reliability and convergence. This paper proposes a hybrid Lyapunov-DLD framework that integrates Lyapunov Drift-Plus-Penalty (LDPP) control with Dual Lagrange Decomposition (DLD) to enable self-organizing network (SON) capabilities for adaptive Open Radio Unit (O-RU) resource allocation, thereby ensuring timely user updates from the server. The LDPP mechanism dynamically allocates ORU computational and bandwidth resources in response to real-time environmental drift, while Projected Momentum Gradient Descent (PMGD) accelerates convergence and optimizes penalty adaptation. Leveraging LDPP-provisioned bandwidth, DLD allocates transmission power to users based on channel state information (CSI), ensuring reliable model weight delivery. The user-side optimization problem is addressed through a Proximal Policy Optimization (PPO) algorithm integrated with the Douglas-Rachford Federated Learning (FeDR) model, which stabilizes local training and mitigates divergence arising from data heterogeneity. Experimental results demonstrate a 1.2% improvement in convergence, a 0.5% increase in accuracy, a 0.5% gain in scalability, and a 1.6% higher signal-to-noise ratio (SNR), along with 0.10% lower latency, 0.02% fewer retransmissions, and 0.3% lower energy consumption compared with the FedProx, FedADMM, and FL-MEC baselines.