  Federated Learning (FL) distributes machine learning (ML) training across
many edge devices to reduce data transfer overhead and protect data privacy.
Since FL model training may span millions of devices and is thus
resource-intensive, prior work has focused on improving its resource efficiency
to optimize time-to-accuracy. However, prior work generally treats all
resources the same, while, in practice, they may incur widely different costs,
which instead motivates optimizing cost-to-accuracy. To address the problem, we
design CEFL, which uses adaptive cost-aware client selection policies to
optimize an arbitrary cost metric when training FL models. Our policies extend
and combine prior work on utility-based client selection and critical learning
periods by making them cost-aware. We demonstrate CEFL by designing
carbon-efficient FL, where energy's carbon-intensity is the cost, and show that
it i) reduces carbon emissions by 93\% and reduces training time by 50%
compared to random client selection and ii) reduces carbon emissions by 80%,
while only increasing training time by 38%, compared to a state-of-the-art
approach that optimizes training time.
