There is a growing interest in the decentralized optimization framework that goes under the name of Federated Learning (FL). In particular, much attention is being turned to FL scenarios where the network is strongly heterogeneous in terms of communication resources (e.g., bandwidth) and data distribution. In these cases, communication between local machines (agents) and the central server (Master) is a main consideration. In this work, we present an original communication-constrained Newton-type (NT) algorithm designed to accelerate FL in such heterogeneous scenarios. The algorithm is by design robust to non i.i.d. data distributions, handles heterogeneity of agents' communication resources (CRs), only requires sporadic Hessian computations, and achieves super-linear convergence. This is possible thanks to an incremental strategy, based on a singular value decomposition (SVD) of the local Hessian matrices, which exploits (possibly) outdated second-order information. The proposed solution is thoroughly validated on real datasets by assessing (i) the number of communication rounds required for convergence, (ii) the overall amount of data transmitted and (iii) the number of local Hessian computations required. For all these metrics, the proposed approach shows superior performance against state-of-the art techniques like GIANT and FedNL.

本研究提出了 SHED 算法，这是一种专门用于加速异构场景中的联邦学习的通信受限牛顿型算法，具有对非独立同分布数据分布的鲁棒性，处理了代理通信资源的异构性，并实现了超线性收敛。

SHED：一种基于增量 Hessian 特征向量共享的联邦学习牛顿类算法