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 epsilon-stochastic first-order stationary point with O(epsilon-4) 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.