Most federated learning (FL) approaches assume a fixed device set. However, real-world scenarios often involve devices dynamically joining or leaving the system, driven by, e.g., user mobility patterns or handovers across cell boundaries. This dynamic setting introduces unique challenges: (1) the optimization objective evolves with the active device set, unlike traditional FL's static objective; and (2) the current global model may no longer serve as an effective initialization for subsequent rounds, potentially hindering adaptation, delaying convergence, and reducing resource efficiency. To address these challenges, we first provide a convergence analysis for FL under a dynamic device set, accounting for factors such as gradient noise, local training iterations, and data heterogeneity. Building on this analysis, we propose a model initialization algorithm that enables rapid adaptation whenever devices join or leave the network. Our key idea is to compute a weighted average of previous global models, guided by gradient similarity, to prioritize models trained on data distributions that closely align with the current device set, thereby accelerating recovery from distribution shifts in fewer training rounds. This plug-and-play algorithm is designed to integrate seamlessly with existing FL methods, offering broad applicability. Experiments demonstrate that our approach achieves convergence speedups typically an order of magnitude or more compared to baselines, which we show drastically reduces energy consumption to reach a target accuracy.

翻译：大多数联邦学习（FL）方法假设设备集合固定不变。然而，现实场景中设备常因用户移动模式或跨小区切换等因素动态加入或离开系统。这种动态环境带来独特挑战：（1）优化目标随活跃设备集合变化而演变，不同于传统FL的静态目标；（2）当前全局模型可能不再作为后续训练轮次的有效初始化，可能阻碍适应过程、延迟收敛并降低资源效率。为应对这些挑战，我们首先对动态设备集合下的FL进行收敛性分析，综合考虑梯度噪声、本地训练迭代次数及数据异质性等因素。基于此分析，我们提出一种模型初始化算法，能够在设备加入或离开网络时实现快速适应。其核心思想是通过梯度相似度指导，计算历史全局模型的加权平均值，优先选择与当前设备集合数据分布高度匹配的模型，从而以更少训练轮次加速从分布偏移中的恢复。这种即插即用算法可与现有FL方法无缝集成，具有广泛适用性。实验表明，相较于基线方法，本方法通常能实现数量级或更高的收敛加速，我们证明这能显著降低达到目标精度所需的能耗。