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Decentralized minimax optimization has been actively studied in the past fewyears due to its application in a wide range of machine learning models.However, the current theoretical understanding of its convergence rate is farfrom satisfactory since existing works only focus on thenonconvex-strongly-concave problem. This motivates us to study decentralizedminimax optimization algorithms for the nonconvex-nonconcave problem. To thisend, we develop two novel decentralized stochastic variance-reduced gradientdescent ascent algorithms for the finite-sum nonconvex-nonconcave problem thatsatisfies the Polyak-{\L}ojasiewicz (PL) condition. In particular, ourtheoretical analyses demonstrate how to conduct local updates and performcommunication to achieve the linear convergence rate. To the best of ourknowledge, this is the first work achieving linear convergence rates fordecentralized nonconvex-nonconcave problems. Finally, we verify the performanceof our algorithms on both synthetic and real-world datasets. The experimentalresults confirm the efficacy of our algorithms.

Can Decentralized Stochastic Minimax Optimization Algorithms Converge Linearly for Finite-Sum Nonconvex-Nonconcave Problems?