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）已被公认为实现通信高效协同学习的关键框架。然而，大多数理论与实证研究均基于客户端可访问预收集数据集的假设，对客户端持续收集数据的场景研究有限。在许多现实应用中，尤其是当数据由物理或生物过程生成时，客户端数据流常被建模为非平稳马尔可夫过程。与标准的独立同分布采样不同，由于客户端样本随时间存在统计依赖性，基于马尔可夫数据流的联邦学习性能仍鲜为人知。本文探究联邦学习是否仍能支持基于马尔可夫数据流的协同学习。具体而言，我们分析了小批量随机梯度下降法、局部随机梯度下降法以及带动量的局部随机梯度下降法变体的性能。在标准假设与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，其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。