  We propose a novel single-loop decentralized algorithm called DGDA-VR for
solving the stochastic nonconvex strongly-concave minimax problem over a
connected network of $M$ agents. By using stochastic first-order oracles to
estimate the local gradients, we prove that our algorithm finds an
$\epsilon$-accurate solution with $\mathcal{O}(\epsilon^{-3})$ sample
complexity and $\mathcal{O}(\epsilon^{-2})$ communication complexity, both of
which are optimal and match the lower bounds for this class of problems. Unlike
competitors, our algorithm does not require multiple communications for the
convergence results to hold, making it applicable to a broader computational
environment setting. To the best of our knowledge, this is the first such
algorithm to jointly optimize the sample and communication complexities for the
problem considered here.
