A Doubly Smoothed Decentralized Stochastic Minimax Optimization Algorithm

Decentralized stochastic minimax optimization has recently attracted significant attention due to its applications in machine learning. However, existing state-of-the-art methods use learning rates of different scales for the primal and dual variables, making them difficult to tune in practice. To address this problem, this paper proposes a novel doubly smoothed decentralized stochastic minimax algorithm. Specifically, in terms of algorithm design, we update both the primal and dual variables using smoothed gradients and introduce novel approaches to handle the computation and communication of the auxiliary variables introduced by the smoothing technique. On the theoretical side, for nonconvex-PL problems, our convergence analysis reveals that the learning rates for the primal and dual variables are of the same scale. Moreover, the order of the condition number in our convergence rate is improved to $O(\kappa^{3/2})$. To the best of our knowledge, this is the first time it has been improved to such a favorable order. Finally, extensive experimental results validate the effectiveness of our algorithm.