Beyond Parameter Consensus: Communication-Efficient Personalized Federated ADMM with One-Bit Consensus

Federated learning enables collaborative model training without sharing raw data, but repeated exchanges of high-dimensional model parameters incur substantial communication costs. Under heterogeneous data distributions, reducing these costs while maintaining effective cross-client collaboration and client-specific adaptation remains challenging. To address this challenge, we propose Federated ADMM with One-bit Consensus (FICO), a communication-efficient personalized federated learning framework. FICO relaxes exact parameter consensus to one-bit consensus over low-dimensional model representations, preserving client-specific variations while coordinating clients through a shared one-bit code. We develop a proximal ADMM algorithm that alternates between personalized model optimization and shared consensus code updates. Each client transmits one-bit signs of local cost differences together with a single amplitude scalar, allowing the server to select the shared code using compact messages while full-precision model variables remain local. Theoretical analysis establishes convergence to stationarity under suitable regularity and error conditions. Experimental results demonstrate that FICO achieves a more favorable trade-off between communication cost and personalized model accuracy than the evaluated baselines.