Federated learning (FL) is now recognized as a key framework for communication-efficient collaborative learning. Most theoretical and empirical studies, however, rely on the assumption that clients have access to pre-collected data sets, with limited investigation into scenarios where clients continuously collect data. In many real-world applications, particularly when data is generated by physical or biological processes, client data streams are often modeled by non-stationary Markov processes. Unlike standard i.i.d. sampling, the performance of FL with Markovian data streams remains poorly understood due to the statistical dependencies between client samples over time. In this paper, we investigate whether FL can still support collaborative learning with Markovian data streams. Specifically, we analyze the performance of Minibatch SGD, Local SGD, and a variant of Local SGD with momentum. We answer affirmatively under standard assumptions and smooth non-convex client objectives: the sample complexity is proportional to the inverse of the number of clients with a communication complexity comparable to the i.i.d. scenario. However, the sample complexity for Markovian data streams remains higher than for i.i.d. sampling.

翻译：联邦学习（FL）已被公认为一种通信高效的协作学习关键框架。然而，大多数理论和实证研究均基于客户端能够访问预先收集的数据集这一假设，对客户端持续收集数据的场景研究有限。在许多实际应用中，特别是当数据由物理或生物过程生成时，客户端数据流通常由非平稳马尔可夫过程建模。与标准的独立同分布采样不同，由于客户端样本间随时间存在统计依赖性，马尔可夫数据流下的联邦学习性能仍鲜为人知。本文探讨了联邦学习是否仍能支持基于马尔可夫数据流的协作学习。具体而言，我们分析了小批量随机梯度下降、局部随机梯度下降以及一种带动量的局部随机梯度下降变体的性能。在标准假设和平滑非凸客户端目标函数下，我们给出了肯定回答：样本复杂度与客户端数量成反比，且通信复杂度与独立同分布场景相当。然而，马尔可夫数据流的样本复杂度仍高于独立同分布采样。