Appears in collection : 11e Journée Statistique et Informatique pour la Science des Données à Paris-Saclay

In federated learning, multiple users collaboratively train a machine learning model without sharing local data. To reduce communication, users perform multiple local stochastic gradient steps that are then aggregated by a central server. However, due to data heterogeneity, local training introduces bias. In this talk, I will present a novel interpretation of the Federated Averaging algorithm, establishing its convergence to a stationary distribution. By analyzing this distribution, we show that the bias consists of two components: one due to heterogeneity and another due to gradient stochasticity. I will then extend this analysis to the Scaffold algorithm, demonstrating that it effectively mitigates heterogeneity bias but not stochasticity bias. Finally, we show that both algorithms achieve linear speed-up in the number of agents, a key property in federated stochastic optimization.