Decentralized Personalized Federated Learning with Compressed Messages via Finite-Time Quantized Coordination

Decentralized Federated Learning (DFL) enables privacy-preserving collaborative training without a central server. However, it faces two major challenges: statistical data heterogeneity, which degrades global model performance on local tasks, and limited communication bandwidth, which hinders collaboration and degrades model accuracy. To address these issues, we propose Q-pFedMe, a decentralized personalized FL algorithm with quantized communication. Q-pFedMe decouples local personalized model optimization from global reference learning using Moreau envelopes. Furthermore, it embeds fixed-point quantization into finite-time averaging, making all nodes reach exact agreement on a common quantized aggregate. We theoretically prove that Q-pFedMe converges linearly to a quantization-dependent neighborhood of the optimal solution for strongly convex objectives, and has an $\mathcal{O}(1/R)$ optimization term with an explicit error floor for smooth non-convex objectives. We also derive a finite-time upper bound on the number of communication steps required by the quantized average consensus subroutine at each global round. Experiments on Synthetic, MNIST, and CIFAR-10 show that Q-pFedMe achieves accuracy comparable to centralized unquantized pFedMe. Additional CIFAR-100 experiments on two directed topologies demonstrate the highest personalized accuracy and lowest per-transmission payload among the evaluated decentralized baselines. Our code is available at https://anonymous.4open.science/r/N8HgpH8UoWHorEt/.