Streaming Federated Learning with Markovian Data

2025-03-24

AI Summary

This work investigates the feasibility and convergence of federated learning (FL) under non-stationary, streaming data generated by time-varying Markov processes—characterized by non-i.i.d., temporal dependence, and sequential arrival. Addressing the limitation of classical FL theory, which assumes static i.i.d. data, we establish the first theoretical framework for FL over non-stationary Markov data streams. We analyze the convergence behavior of mini-batch SGD, Local SGD, and their momentum variants under this setting. Leveraging tools from stochastic optimization, Markov chain mixing-time analysis, and distributed convergence proofs, we derive rigorous convergence bounds for smooth non-convex objectives. Our results show that sample complexity improves with increasing numbers of clients, while communication complexity matches that of the i.i.d. case. These findings confirm FL’s scalability in dynamic, streaming edge environments and provide foundational theoretical guarantees for real-time edge intelligence.

Technology Category

• Machine Learning: Distributed Machine Learning & Federated Learning
• Search and Optimization: Non-convex Optimization
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Federated Web and WoT systems, including distributed, federated and edge-based data processing
• User Modeling, Personalization and Recommendation: Federated recommendation systems and personalization
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

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.

Problem

• Investigates FL feasibility with non-stationary Markovian data streams
• Compares sample complexity of FL algorithms under Markovian vs i.i.d. data
• Analyzes communication efficiency of Local SGD variants in streaming FL

Innovation

• Streaming FL with non-stationary Markov data
• Analyzed Minibatch SGD, Local SGD variants
• Sample complexity scales with client count