We consider the problem of minimizing the convergence time for decentralized federated learning (DFL) in wireless networks under broadcast communications, with focus on mixing matrix design. The mixing matrix is a critical hyperparameter for DFL that simultaneously controls the convergence rate across iterations and the communication demand per iteration, both strongly influencing the convergence time. Although the problem has been studied previously, existing solutions are mostly designed for decentralized parallel stochastic gradient descent (D-PSGD), which requires the mixing matrix to be symmetric and doubly stochastic. These constraints confine the activated communication graph to undirected (i.e., bidirected) graphs, which limits design flexibility. In contrast, we consider mixing matrix design for stochastic gradient push (SGP), which allows asymmetric mixing matrices and hence directed communication graphs. By analyzing how the convergence rate of SGP depends on the mixing matrices, we extract an objective function that explicitly depends on graph-theoretic parameters of the activated communication graph, based on which we develop an efficient design algorithm with performance guarantees. Our evaluations based on real data show that the proposed solution can notably reduce the convergence time compared to the state of the art without compromising the quality of the trained model.

翻译：我们研究无线网络中广播通信场景下，面向降低去中心化联邦学习（DFL）收敛时间的问题，重点聚焦于混合矩阵的设计。混合矩阵是DFL的关键超参数，它同时控制迭代间的收敛速率与单次迭代的通信需求，两者均对收敛时间产生重要影响。尽管该问题已有前期研究，现有解决方案主要针对去中心化并行随机梯度下降（D-PSGD）设计，要求混合矩阵具有对称性和双随机性。这些约束将激活通信图限制为无向（即双向）图，从而降低了设计灵活性。相比之下，我们针对随机梯度推送（SGP）算法研究混合矩阵设计，该算法可兼容非对称混合矩阵，进而支持有向通信图。通过分析SGP的收敛速率与混合矩阵的依赖关系，我们提取出显式依赖于激活通信图谱理论参数的目标函数，并据此开发出具有性能保证的高效设计算法。基于真实数据的评估表明，与现有最优方案相比，本方案能在不影响训练模型质量的前提下显著缩短收敛时间。