标题： 共识ALADIN：一种分布式优化框架及其在联邦学习中的应用 显示英文标题

标题： Consensus ALADIN: A Framework for Distributed Optimization and Its Application in Federated Learning

摘要： 本文研究用于解决非凸分布式共识优化问题的算法。由于典型ALADIN（典型增广拉格朗日交替方向不精确牛顿方法，简称T-ALADIN）[1]是一个在处理非凸分布式优化问题方面表现良好的算法，直接将T-ALADIN应用于共识问题是一种自然的方法。然而，T-ALADIN通常会导致高通信和计算开销，这使得这种方法效率远不够。在本文中，我们提出ALADIN家族的一个新变种，称为共识ALADIN（简称C-ALADIN）。C-ALADIN继承了T-ALADIN的所有优点，例如局部线性或超线性收敛速率以及对非凸优化问题的局部收敛保证；此外，C-ALADIN在通信效率和计算效率方面提供了独特的改进。此外，与共识ADMM（乘子交替方向法）[3]相比，C-ALADIN涉及一个简化版本，在没有二阶信息帮助的情况下也表现出显著的收敛性能。我们还提出了C-ALADIN的一个实用版本，命名为FedALADIN，它无缝服务于新兴的联邦学习应用，扩展了我们提出的C-ALADIN的应用范围。我们提供了数值实验来证明C-ALADIN的有效性。结果表明，C-ALADIN在收敛性能方面有显著改进。 显示英文摘要

摘要： 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) [1] 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) [3], 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.