  Federated learning (FL) approaches for saddle point problems (SPP) have
recently gained in popularity due to the critical role they play in machine
learning (ML). Existing works mostly target smooth unconstrained objectives in
Euclidean space, whereas ML problems often involve constraints or non-smooth
regularization, which results in a need for composite optimization. Addressing
these issues, we propose Federated Dual Extrapolation (FeDualEx), an extra-step
primal-dual algorithm, which is the first of its kind that encompasses both
saddle point optimization and composite objectives under the FL paradigm. Both
the convergence analysis and the empirical evaluation demonstrate the
effectiveness of FeDualEx in these challenging settings. In addition, even for
the sequential version of FeDualEx, we provide rates for the stochastic
composite saddle point setting which, to our knowledge, are not found in prior
literature.
