  Training a machine learning model with federated edge learning (FEEL) is
typically time-consuming due to the constrained computation power of edge
devices and limited wireless resources in edge networks. In this paper, the
training time minimization problem is investigated in a quantized FEEL system,
where the heterogeneous edge devices send quantized gradients to the edge
server via orthogonal channels. In particular, a stochastic quantization scheme
is adopted for compression of uploaded gradients, which can reduce the burden
of per-round communication but may come at the cost of increasing number of
communication rounds. The training time is modeled by taking into account the
communication time, computation time and the number of communication rounds.
Based on the proposed training time model, the intrinsic trade-off between the
number of communication rounds and per-round latency is characterized.
Specifically, we analyze the convergence behavior of the quantized FEEL in
terms of the optimality gap. Further, a joint data-and-model-driven fitting
method is proposed to obtain the exact optimality gap, based on which the
closed-form expressions for the number of communication rounds and the total
training time are obtained. Constrained by total bandwidth, the training time
minimization problem is formulated as a joint quantization level and bandwidth
allocation optimization problem. To this end, an algorithm based on alternating
optimization is proposed, which alternatively solves the subproblem of
quantization optimization via successive convex approximation and the
subproblem of bandwidth allocation via bisection search. With different
learning tasks and models, the validation of our analysis and the near-optimal
performance of the proposed optimization algorithm are demonstrated by the
experimental results.
