Nonconvex Nonconcave Problem

Nonconvex-nonconcave minimax optimization problems, arising frequently in machine learning applications like GANs and federated learning, pose significant challenges due to the lack of convexity in both the objective function and its dual. Current research focuses on developing efficient decentralized and federated algorithms, such as variance-reduced gradient descent ascent methods and extragradient-type algorithms, to find approximate solutions, often leveraging techniques like communication compression and partial client participation to improve scalability. These advancements are crucial for tackling large-scale datasets and heterogeneous computational environments, impacting the efficiency and applicability of various machine learning models.