A decentralized adaptive method with consensus step for non-convex non-concave min-max optimization problems

To solve min–max optimization problems, decentralized adaptive methods have been presented over multi-agent networks. In the non-convex non-concave structure, however, existing decentralized adaptive min–max methods may be divergence due to the inconsistency in the adaptive learning rate. To address this issue, we propose a novel decentralized adaptive algorithm named DADAMC, where the consensus protocol is introduced to synchronize the adaptive learning rates of all agents. Furthermore, we rigorously analyze that DADAMC converges to an $ϵ$-stochastic first-order stationary point with $O\left({ϵ}^{-4}\right)$ complexity. In addition, we also conduct experiments to verify the performance of DADAMC for solving a robust regression problem. The experimental results show that DADAMC outperforms state-of-the-art decentralized min–max algorithms.