  In this paper we propose the federated private local training algorithm
(Fed-PLT) for federated learning, to overcome the challenges of (i) expensive
communications and (ii) privacy preservation. We address (i) by allowing for
both partial participation and local training, which significantly reduce the
number of communication rounds between the central coordinator and computing
agents. The algorithm matches the state of the art in the sense that the use of
local training demonstrably does not impact accuracy. Additionally, agents have
the flexibility to choose from various local training solvers, such as
(stochastic) gradient descent and accelerated gradient descent. Further, we
investigate how employing local training can enhance privacy, addressing point
(ii). In particular, we derive differential privacy bounds and highlight their
dependence on the number of local training epochs. We assess the effectiveness
of the proposed algorithm by comparing it to alternative techniques,
considering both theoretical analysis and numerical results from a
classification task.
