We consider the design of mixing matrices to minimize the operation cost for decentralized federated learning (DFL) in wireless networks, with focus on minimizing the maximum per-node energy consumption. As a critical hyperparameter for DFL, the mixing matrix controls both the convergence rate and the needs of agent-to-agent communications, and has thus been studied extensively. However, existing designs mostly focused on minimizing the communication time, leaving open the minimization of per-node energy consumption that is critical for energy-constrained devices. This work addresses this gap through a theoretically-justified solution for mixing matrix design that aims at minimizing the maximum per-node energy consumption until convergence, while taking into account the broadcast nature of wireless communications. Based on a novel convergence theorem that allows arbitrarily time-varying mixing matrices, we propose a multi-phase design framework that activates time-varying communication topologies under optimized budgets to trade off the per-iteration energy consumption and the convergence rate while balancing the energy consumption across nodes. Our evaluations based on real data have validated the efficacy of the proposed solution in combining the low energy consumption of sparse mixing matrices and the fast convergence of dense mixing matrices.

翻译：本文研究无线网络中用于最小化去中心化联邦学习（DFL）运行成本的混合矩阵设计问题，重点关注最小化最大单节点能耗。作为DFL的关键超参数，混合矩阵同时控制着收敛速度与节点间通信需求，因而已被广泛研究。然而，现有设计主要集中于最小化通信时间，尚未解决对能量受限设备至关重要的单节点能耗最小化问题。本研究通过提出一种理论支撑的混合矩阵设计方案来填补这一空白，该方案旨在考虑无线通信广播特性的同时，最小化收敛前的最大单节点能耗。基于允许任意时变混合矩阵的新颖收敛定理，我们提出一种多阶段设计框架，该框架在优化预算下激活时变通信拓扑，以权衡单轮迭代能耗与收敛速度，同时实现节点间能耗均衡。基于真实数据的评估验证了所提方案在融合稀疏混合矩阵的低能耗特性与稠密混合矩阵的快速收敛性方面的有效性。