  Federated Learning (FL) has opened the opportunity for collaboratively
training machine learning models on heterogeneous mobile or Edge devices while
keeping local data private.With an increase in its adoption, a growing concern
is related to its economic and environmental cost (as is also the case for
other machine learning techniques).Unfortunately, little work has been done to
optimize its energy consumption or emissions of carbon dioxide or equivalents,
as energy minimization is usually left as a secondary objective.In this paper,
we investigate the problem of minimizing the energy consumption of FL training
on heterogeneous devices by controlling the workload distribution.We model this
as the Minimal Cost FL Schedule problem, a total cost minimization problem with
identical, independent, and atomic tasks that have to be assigned to
heterogeneous resources with arbitrary cost functions.We propose a
pseudo-polynomial optimal solution to the problem based on the previously
unexplored Multiple-Choice Minimum-Cost Maximal Knapsack Packing Problem.We
also provide four algorithms for scenarios where cost functions are
monotonically increasing and follow the same behavior.These solutions are
likewise applicable on the minimization of other kinds of costs, and in other
one-dimensional data partition problems.
