Minimax Problem

Minimax problems, which involve finding a saddle point where one function is minimized and another is maximized, are central to many machine learning applications, including generative adversarial networks and robust optimization. Current research focuses on developing efficient algorithms, particularly gradient-based methods like gradient descent-ascent (GDA) and its variants (e.g., two-timescale GDA, extragradient methods), to solve these problems, especially in nonconvex-concave or even nonconvex-nonconcave settings. These advancements address challenges like parameter-free optimization, distributed computation, and handling constraints (including those on Riemannian manifolds), leading to improved convergence rates and reduced computational complexity. The resulting algorithms have significant implications for training large-scale models and improving the robustness and efficiency of machine learning systems.