  In this paper, the problem of energy efficient transmission and computation
resource allocation for federated learning (FL) over wireless communication
networks is investigated. In the considered model, each user exploits limited
local computational resources to train a local FL model with its collected data
and, then, sends the trained FL model to a base station (BS) which aggregates
the local FL model and broadcasts it back to all of the users. Since FL
involves an exchange of a learning model between users and the BS, both
computation and communication latencies are determined by the learning accuracy
level. Meanwhile, due to the limited energy budget of the wireless users, both
local computation energy and transmission energy must be considered during the
FL process. This joint learning and communication problem is formulated as an
optimization problem whose goal is to minimize the total energy consumption of
the system under a latency constraint. To solve this problem, an iterative
algorithm is proposed where, at every step, closed-form solutions for time
allocation, bandwidth allocation, power control, computation frequency, and
learning accuracy are derived. Since the iterative algorithm requires an
initial feasible solution, we construct the completion time minimization
problem and a bisection-based algorithm is proposed to obtain the optimal
solution, which is a feasible solution to the original energy minimization
problem. Numerical results show that the proposed algorithms can reduce up to
59.5% energy consumption compared to the conventional FL method.
