  Federated learning (FL), a novel branch of distributed machine learning (ML),
develops global models through a private procedure without direct access to
local datasets. However, it is still possible to access the model updates
(gradient updates of deep neural networks) transferred between clients and
servers, potentially revealing sensitive local information to adversaries using
model inversion attacks. Differential privacy (DP) offers a promising approach
to addressing this issue by adding noise to the parameters. On the other hand,
heterogeneities in data structure, storage, communication, and computational
capabilities of devices can cause convergence problems and delays in developing
the global model. A personalized weighted averaging of local parameters based
on the resources of each device can yield a better aggregated model in each
round. In this paper, to efficiently preserve privacy, we propose a
personalized DP framework that injects noise based on clients' relative impact
factors and aggregates parameters while considering heterogeneities and
adjusting properties. To fulfill the DP requirements, we first analyze the
convergence boundary of the FL algorithm when impact factors are personalized
and fixed throughout the learning process. We then further study the
convergence property considering time-varying (adaptive) impact factors.
