  Federated learning (FL) enables learning from decentralized privacy-sensitive
data, with computations on raw data confined to take place at edge clients.
This paper introduces mixed FL, which incorporates an additional loss term
calculated at the coordinating server (while maintaining FL's private data
restrictions). There are numerous benefits. For example, additional datacenter
data can be leveraged to jointly learn from centralized (datacenter) and
decentralized (federated) training data and better match an expected inference
data distribution. Mixed FL also enables offloading some intensive computations
(e.g., embedding regularization) to the server, greatly reducing communication
and client computation load. For these and other mixed FL use cases, we present
three algorithms: PARALLEL TRAINING, 1-WAY GRADIENT TRANSFER, and 2-WAY
GRADIENT TRANSFER. We state convergence bounds for each, and give intuition on
which are suited to particular mixed FL problems. Finally we perform extensive
experiments on three tasks, demonstrating that mixed FL can blend training data
to achieve an oracle's accuracy on an inference distribution, and can reduce
communication and computation overhead by over 90%. Our experiments confirm
theoretical predictions of how algorithms perform under different mixed FL
problem settings.
