Decentralized Accelerated Nonconvex Minimax Optimization via Exact Diffusion

Exact Diffusion is a powerful algorithm for decentralized minimization problems over multi-agent networks, showing significant advantages over gradient-tracking methods, particularly in sparsely connected networks. Despite its success, this technique has remained largely unexplored in the context of decentralized minimax optimization, leaving it unclear whether its benefits extend to this setting. To address this gap, we propose a new algorithm that integrates Exact Diffusion with accelerated momentum for nonconvex-PL minimax problems. We provide a theoretical analysis showing that our method achieves a per-agent sample complexity of O(κ3/Kε3+κ2/(1−λ)2ε2) for finding an ε-stationary point, thereby outperforming existing gradient-tracking-based minimax algorithms, where κ is the condition number, K is the number of agents, and λ is the mixing rate of the network. Numerical experiments support our theoretical findings