Jointly Improving the Sample and Communication Complexities in Decentralized Stochastic Minimax Optimization

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.