Do ED and EXTRA retain their advantages in decentralized minimax optimization

Determine whether the decentralized bias-correction strategies Exact Diffusion (ED) and EXTRA, which achieve improved rates for decentralized minimization, also retain their advantages when applied to decentralized nonconvex Polyak–Łojasiewicz (PL) minimax optimization over multi-agent networks, particularly under sparse communication topologies and heterogeneous local data.

Background

Gradient tracking (GT) is widely used in decentralized minimax optimization to mitigate data heterogeneity, but it may not achieve state-of-the-art performance on sparse networks. In decentralized minimization, alternative strategies such as Exact Diffusion (ED) and EXTRA have shown better rates than GT.

However, these alternatives have not been thoroughly investigated for minimax problems, creating uncertainty about whether their benefits extend to the minimax setting. This motivates examining whether ED and EXTRA can also deliver improved performance for decentralized nonconvex PL minimax optimization, which is the focus of this work.

References

Yet these alternative methods remain underexplored in the minimax setting, and it is uncertain whether their advantages carry over to the minimax optimization domain.

— DAMA: A Unified Accelerated Approach for Decentralized Nonconvex Minimax Optimization-Part I: Algorithm Development and Results  (2512.13920 - Cai et al., 15 Dec 2025) in Section 1, Introduction