A Localized Primal-Dual Method for Centralized/Decentralized Federated Learning Robust to Data Heterogeneity

Generalized Edge-Consensus Learning (G-ECL) is a primal-dual method to solve loss-sum minimization problems. We propose Local Generalized Edge-Consensus Learning (Local G-ECL) as an extension of previous G-ECL, aiming to be a decentralized/centralized FL algorithm robust to heterogeneous data sets with a large number of local updates. Our contributions are as follows: (C1) success in theoretical gradient norm convergence analysis nearly independently of data heterogeneity, and (C2) equivalency proof between our primal-dual Local G-ECL and a pure primal Stochastic Controlled Averaging (SCAFFOLD) algorithm in centralized settings, where the difference in the initial local model for each round is ignored. Numerical experiments using image classification tests validated that Local G-ECL is robust to heterogeneous data with a large number of local updates.