  Federated learning (FL) is a distributed machine learning (ML) framework
where multiple clients collaborate to train a model without exposing their
private data. FL involves cycles of local computations and bi-directional
communications between the clients and server. To bolster data security during
this process, FL algorithms frequently employ a differential privacy (DP)
mechanism that introduces noise into each client's model updates before
sharing. However, while enhancing privacy, the DP mechanism often hampers
convergence performance. In this paper, we posit that an optimal balance exists
between the number of local steps and communication rounds, one that maximizes
the convergence performance within a given privacy budget. Specifically, we
present a proof for the optimal number of local steps and communication rounds
that enhance the convergence bounds of the DP version of the ScaffNew
algorithm. Our findings reveal a direct correlation between the optimal number
of local steps, communication rounds, and a set of variables, e.g the DP
privacy budget and other problem parameters, specifically in the context of
strongly convex optimization. We furthermore provide empirical evidence to
validate our theoretical findings.
