  Decentralized minimax optimization has been actively studied in the past few
years due to its application in a wide range of machine learning models.
However, the current theoretical understanding of its convergence rate is far
from satisfactory since existing works only focus on the
nonconvex-strongly-concave problem. This motivates us to study decentralized
minimax optimization algorithms for the nonconvex-nonconcave problem. To this
end, we develop two novel decentralized stochastic variance-reduced gradient
descent ascent algorithms for the finite-sum nonconvex-nonconcave problem that
satisfies the Polyak-{\L}ojasiewicz (PL) condition. In particular, our
theoretical analyses demonstrate how to conduct local updates and perform
communication to achieve the linear convergence rate. To the best of our
knowledge, this is the first work achieving linear convergence rates for
decentralized nonconvex-nonconcave problems. Finally, we verify the performance
of our algorithms on both synthetic and real-world datasets. The experimental
results confirm the efficacy of our algorithms.
