  In Federated Learning (FL), with parameter aggregated by a central node, the
communication overhead is a substantial concern. To circumvent this limitation
and alleviate the single point of failure within the FL framework, recent
studies have introduced Decentralized Federated Learning (DFL) as a viable
alternative. Considering the device heterogeneity, and energy cost associated
with parameter aggregation, in this paper, the problem on how to efficiently
leverage the limited resources available to enhance the model performance is
investigated. Specifically, we formulate a problem that minimizes the loss
function of DFL while considering energy and latency constraints. The proposed
solution involves optimizing the number of local training rounds across diverse
devices with varying resource budgets. To make this problem tractable, we first
analyze the convergence of DFL with edge devices with different rounds of local
training. The derived convergence bound reveals the impact of the rounds of
local training on the model performance. Then, based on the derived bound, the
closed-form solutions of rounds of local training in different devices are
obtained. Meanwhile, since the solutions require the energy cost of aggregation
as low as possible, we modify different graph-based aggregation schemes to
solve this energy consumption minimization problem, which can be applied to
different communication scenarios. Finally, a DFL framework which jointly
considers the optimized rounds of local training and the energy-saving
aggregation scheme is proposed. Simulation results show that, the proposed
algorithm achieves a better performance than the conventional schemes with
fixed rounds of local training, and consumes less energy than other traditional
aggregation schemes.
