  In this article, we address the problem of federated learning in the presence
of stragglers. For this problem, a coded federated learning framework has been
proposed, where the central server aggregates gradients received from the
non-stragglers and gradient computed from a privacy-preservation global coded
dataset to mitigate the negative impact of the stragglers. However, when
aggregating these gradients, fixed weights are consistently applied across
iterations, neglecting the generation process of the global coded dataset and
the dynamic nature of the trained model over iterations. This oversight may
result in diminished learning performance. To overcome this drawback, we
propose a new method named adaptive coded federated learning (ACFL). In ACFL,
before the training, each device uploads a coded local dataset with additive
noise to the central server to generate a global coded dataset under privacy
preservation requirements. During each iteration of the training, the central
server aggregates the gradients received from the non-stragglers and the
gradient computed from the global coded dataset, where an adaptive policy for
varying the aggregation weights is designed. Under this policy, we optimize the
performance in terms of privacy and learning, where the learning performance is
analyzed through convergence analysis and the privacy performance is
characterized via mutual information differential privacy. Finally, we perform
simulations to demonstrate the superiority of ACFL compared with the
non-adaptive methods.
