This paper proposes a fully decentralized federated learning (FL) scheme for Internet of Everything (IoE) devices that are connected via multi-hop networks. Because FL algorithms hardly converge the parameters of machine learning (ML) models, this paper focuses on the convergence of ML models in function spaces. Considering that the representative loss functions of ML tasks e.g, mean squared error (MSE) and Kullback-Leibler (KL) divergence, are convex functionals, algorithms that directly update functions in function spaces could converge to the optimal solution. The key concept of this paper is to tailor a consensus-based optimization algorithm to work in the function space and achieve the global optimum in a distributed manner. This paper first analyzes the convergence of the proposed algorithm in a function space, which is referred to as a meta-algorithm, and shows that the spectral graph theory can be applied to the function space in a manner similar to that of numerical vectors. Then, consensus-based multi-hop federated distillation (CMFD) is developed for a neural network (NN) to implement the meta-algorithm. CMFD leverages knowledge distillation to realize function aggregation among adjacent devices without parameter averaging. An advantage of CMFD is that it works even with different NN models among the distributed learners. Although CMFD does not perfectly reflect the behavior of the meta-algorithm, the discussion of the meta-algorithm's convergence property promotes an intuitive understanding of CMFD, and simulation evaluations show that NN models converge using CMFD for several tasks. The simulation results also show that CMFD achieves higher accuracy than parameter aggregation for weakly connected networks, and CMFD is more stable than parameter aggregation methods.

翻译：本文建议了完全分散化的 Everything (IoE) 网络互联网(IoE) 功能的学习(FL) 方法。 由于 FL 算法几乎无法与机器学习(ML) 模型的参数趋同, 本文侧重于功能空间中 ML 模型的趋同。 考虑到 ML 任务( 平均正方差 ) 和 Kullback- Leiber (KL) 差异 的代表性损失功能, 它们是连接功能, 直接更新功能功能中连接到功能空间中连接到最佳解决方案的算法。 本文的关键概念是将基于共识的优化算法用于在功能空间中工作, 使基于共识的精度优化算法( Law) 用于在功能中工作, 在功能空间中, 将基于精度的精度( MLML) 模型的精度( MLML ) 的精度( ML) 模型的趋同SDMDM 。