  Federated learning is a distributed learning setting where the main aim is to
train machine learning models without having to share raw data but only what is
required for learning. To guarantee training data privacy and high-utility
models, differential privacy and secure aggregation techniques are often
combined with federated learning. However, with fine-grained protection
granularities the currently existing techniques require the parties to
communicate for each local optimisation step, if they want to fully benefit
from the secure aggregation in terms of the resulting formal privacy
guarantees. In this paper, we show how a simple new analysis allows the parties
to perform multiple local optimisation steps while still benefiting from joint
noise scaling when using secure aggregation. We show that our analysis enables
higher utility models with guaranteed privacy protection under limited number
of communication rounds.
