This paper considers the problem of distributed multi-agent learning, where the global aim is to minimize a sum of local objective (empirical loss) functions through local optimization and information exchange between neighbouring nodes. We introduce a Newton-type fully distributed optimization algorithm, Network-GIANT, which is based on GIANT, a Federated learning algorithm that relies on a centralized parameter server. The Network-GIANT algorithm is designed via a combination of gradient-tracking and a Newton-type iterative algorithm at each node with consensus based averaging of local gradient and Newton updates. We prove that our algorithm guarantees semi-global and exponential convergence to the exact solution over the network assuming strongly convex and smooth loss functions. We provide empirical evidence of the superior convergence performance of Network-GIANT over other state-of-art distributed learning algorithms such as Network-DANE and Newton-Raphson Consensus.

翻译：论文摘要：本文研究了分布式多智能体学习问题，其全局目标是通过局部优化和相邻节点间的信息交换，最小化局部目标（经验损失）函数之和。我们提出了一种牛顿型全分布式优化算法——Network-GIANT，该算法基于依赖中央参数服务器的联邦学习算法GIANT。Network-GIANT的设计结合了每个节点的梯度跟踪与牛顿型迭代算法，以及基于一致性的局部梯度和牛顿更新的平均化。我们证明了该算法在强凸且光滑的损失函数假设下，能够保证在网络中半全局且指数级收敛到精确解。我们还提供了实证证据，证明Network-GIANT在收敛性能上优于其他先进分布式学习算法（如Network-DANE和Newton-Raphson Consensus）。