Distributed optimization: designed for federated learning

--Federated Learning (FL), as a distributed collaborative Machine Learning (ML) framework under privacy-preserving constraints, has garnered increasing research attention in cross-organizational data collaboration scenarios. This paper proposes a class of distributed optimization algorithms based on the augmented Lagrangian technique, designed to accommodate diverse communication topologies in both centralized and decentralized FL settings. Furthermore, we develop multiple termination criteria and parameter update mechanisms to enhance computational efficiency, accompanied by rigorous theoretical guarantees of convergence. By generalizing the augmented Lagrangian relaxation through the incorporation of proximal relaxation and quadratic approximation, our framework systematically recovers a broad of classical unconstrained optimization methods, including proximal algorithm, classic gradient descent, and stochastic gradient descent, among others. Notably, the convergence properties of these methods can be naturally derived within the proposed theoretical framework. Numerical experiments demonstrate that the proposed algorithm exhibits strong performance in large-scale settings with significant statistical heterogeneity across clients. Such formulations, commonly referred to as consensus optimization problems, find widespread applications in interdisciplinary domains including distributed ML, collaborative sensing in sensor networks, and distributed parameter estimation [1]. This work was supported in part by the National Natural Science Foundation of China (NSFC) under Grant 52375498, and in part by the Fundamental Research Funds for the Central Universities under Grant 21623111. Ting Qu is with Guangdong International Cooperation Base of Science and Technology for GBA Smart Logistics, Jinan University, Zhuhai 519070, China, also with School of Intelligent Systems Science and Engineering, Jinan University, Zhuhai 519070, China, and also with Institute of Physical Internet, Jinan University, Zhuhai 519070, China (e-mail: quting@jnu.edu.cn).