  This paper analyzes the impact of imperfect communication channels on
decentralized federated learning (D-FL) and subsequently determines the optimal
number of local aggregations per training round, adapting to the network
topology and imperfect channels. We start by deriving the bias of locally
aggregated D-FL models under imperfect channels from the ideal global models
requiring perfect channels and aggregations. The bias reveals that excessive
local aggregations can accumulate communication errors and degrade convergence.
Another important aspect is that we analyze a convergence upper bound of D-FL
based on the bias. By minimizing the bound, the optimal number of local
aggregations is identified to balance a trade-off with accumulation of
communication errors in the absence of knowledge of the channels. With this
knowledge, the impact of communication errors can be alleviated, allowing the
convergence upper bound to decrease throughout aggregations. Experiments
validate our convergence analysis and also identify the optimal number of local
aggregations on two widely considered image classification tasks. It is seen
that D-FL, with an optimal number of local aggregations, can outperform its
potential alternatives by over 10% in training accuracy.
