Xu Du, Jingzhe Wang
This paper investigates algorithms for solving distributed consensus optimization problems that are non-convex. Since Typical ALADIN (Typical Augmented Lagrangian based Alternating Direction Inexact Newton Method, T-ALADIN for short) is a well-performed algorithm treating distributed optimization problems that are non-convex, directly adopting T-ALADIN to those of consensus is a natural approach. However, T-ALADIN typically results in high communication and computation overhead, which makes such an approach far from efficient. In this paper, we propose a new variant of the ALADIN family, coined consensus ALADIN (C-ALADIN for short). C-ALADIN inherits all the good properties of T-ALADIN, such as the local linear or super-linear convergence rate and the local convergence guarantees for non-convex optimization problems; besides, C-ALADIN offers unique improvements in terms of communication efficiency and computational efficiency. Moreover, C-ALADIN involves a reduced version, in comparison with Consensus ADMM (Alternating Direction Method of Multipliers), showing significant convergence performance, even without the help of second-order information. We also propose a practical version of C-ALADIN, named FedALADIN, that seamlessly serves the emerging federated learning applications, which expands the reach of our proposed C-ALADIN. We provide numerical experiments to demonstrate the effectiveness of C-ALADIN. The results show that C-ALADIN has significant improvements in convergence performance.
@misc{du2023consensus,
title={Consensus ALADIN: A Framework for Distributed Optimization and Its Application in Federated Learning},
author={Xu Du and Jingzhe Wang},
year={2023},
eprint={2306.05662},
archivePrefix={arXiv},
primaryClass={math.OC}
}