  Minimax optimization has seen a surge in interest with the advent of modern
applications such as GANs, and it is inherently more challenging than simple
minimization. The difficulty is exacerbated by the training data residing at
multiple edge devices or \textit{clients}, especially when these clients can
have heterogeneous datasets and local computation capabilities. We propose a
general federated minimax optimization framework that subsumes such settings
and several existing methods like Local SGDA. We show that naive aggregation of
heterogeneous local progress results in optimizing a mismatched objective
function -- a phenomenon previously observed in standard federated
minimization. To fix this problem, we propose normalizing the client updates by
the number of local steps undertaken between successive communication rounds.
We analyze the convergence of the proposed algorithm for classes of
nonconvex-concave and nonconvex-nonconcave functions and characterize the
impact of heterogeneous client data, partial client participation, and
heterogeneous local computations. Our analysis works under more general
assumptions on the intra-client noise and inter-client heterogeneity than so
far considered in the literature. For all the function classes considered, we
significantly improve the existing computation and communication complexity
results. Experimental results support our theoretical claims.
