  Federated learning (FL) has emerged as an important machine learning paradigm
where a global model is trained based on the private data from distributed
clients. However, most of existing FL algorithms cannot guarantee the
performance fairness towards different groups because of data distribution
shift over groups. In this paper, we formulate the problem of unified group
fairness on FL, where the groups can be formed by clients (including existing
clients and newly added clients) and sensitive attribute(s). To solve this
problem, we first propose a general fair federated framework. Then we construct
a unified group fairness risk from the view of federated uncertainty set with
theoretical analyses to guarantee unified group fairness on FL. We also develop
an efficient federated optimization algorithm named Federated Mirror Descent
Ascent with Momentum Acceleration (FMDA-M) with convergence guarantee. We
validate the advantages of the FMDA-M algorithm with various kinds of
distribution shift settings in experiments, and the results show that FMDA-M
algorithm outperforms the existing fair FL algorithms on unified group
fairness.
