Continuous-Time Analysis of Federated Averaging
This work provides a novel theoretical framework for federated learning, offering insights into algorithm behavior and generalization, though it is incremental as it builds on existing discrete-time analyses.
The paper tackles the problem of analyzing federated averaging (FedAvg) by extending convergence analysis to a continuous-time setting using stochastic differential equations, establishing convergence guarantees for various loss functions and revealing generalization properties.
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.