Technology Category
Machine Learning: Distributed Machine Learning & Federated LearningReasoning under Uncertainty: Stochastic OptimizationSearch and Optimization: Non-convex Optimization
Continuous-Time Analysis of Federated Averaging
🤖 AI Summary
This paper addresses the convergence and generalization of Federated Averaging (FedAvg) under continuous-time dynamic data streams. We formulate FedAvg as a multivariate stochastic differential equation (SDE), establishing the first rigorous continuous-time convergence theory. Methodologically, we depart from discrete-time iteration frameworks to accommodate heterogeneous data distributions and general loss functions—including non-strongly-convex and nonsmooth cases. Theoretically, we derive sufficient conditions under which the server update asymptotically follows a normal distribution, thereby uncovering FedAvg’s implicit regularization mechanism and its generalization behavior. Key contributions include: (1) the first continuous-time SDE modeling of FedAvg with provable convergence guarantees; (2) convergence analysis extended to broader classes of loss functions; (3) enhanced robustness characterization against statistical heterogeneity; and (4) a novel SDE-based interpretive framework for understanding generalization in federated learning.
Technology Category
Application Category
📝 Abstract
Federated averaging (FedAvg) is a popular algorithm for horizontal federated learning (FL), where samples are gathered across different clients and are not shared with each other or a central server. Extensive convergence analysis of FedAvg exists for the discrete iteration setting, guaranteeing convergence for a range of loss functions and varying levels of data heterogeneity. We extend this analysis to the continuous-time setting where the global weights evolve according to a multivariate stochastic differential equation (SDE), which is the first time FedAvg has been studied from the continuous-time perspective. We use techniques from stochastic processes to establish convergence guarantees under different loss functions, some of which are more general than existing work in the discrete setting. We also provide conditions for which FedAvg updates to the server weights can be approximated as normal random variables. Finally, we use the continuous-time formulation to reveal generalization properties of FedAvg.
Problem
Research questions and friction points this paper is trying to address.
Federated Averaging
Continuous Time Dynamic Data Streams
Time-Varying Data Reliability
Innovation
Methods, ideas, or system contributions that make the work stand out.
Continuous Time Analysis
Stochastic Differential Equations
Streaming Data Performance
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