  The increasing size of data generated by smartphones and IoT devices
motivated the development of Federated Learning (FL), a framework for on-device
collaborative training of machine learning models. First efforts in FL focused
on learning a single global model with good average performance across clients,
but the global model may be arbitrarily bad for a given client, due to the
inherent heterogeneity of local data distributions. Federated multi-task
learning (MTL) approaches can learn personalized models by formulating an
opportune penalized optimization problem. The penalization term can capture
complex relations among personalized models, but eschews clear statistical
assumptions about local data distributions. In this work, we propose to study
federated MTL under the flexible assumption that each local data distribution
is a mixture of unknown underlying distributions. This assumption encompasses
most of the existing personalized FL approaches and leads to federated EM-like
algorithms for both client-server and fully decentralized settings. Moreover,
it provides a principled way to serve personalized models to clients not seen
at training time. The algorithms' convergence is analyzed through a novel
federated surrogate optimization framework, which can be of general interest.
Experimental results on FL benchmarks show that our approach provides models
with higher accuracy and fairness than state-of-the-art methods.

Machine Learning;Artificial Intelligence;Optimization and Control;Machine Learning