arXiv Machine Learning By Tianjiao Luo, Jianfei Chen, Jun Zhu

Controlled-Minimax: Stabilizing Adversarial Optimization via Control Theory

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Controlled-Minimax is a new framework that stabilizes adversarial minimax optimization by modeling training dynamics as a second-order ODE and applying a feedback controller derived from control theory. The method guarantees local exponential stability regardless of the Hessian spectrum, addressing persistent limit cycles and divergence that plague traditional gradient descent-ascent approaches. Experiments on benchmarks such as Dirac-GAN, 2D Gaussian mixtures, Swiss Roll, and StyleGAN2-ada show that Controlled-Minimax suppresses oscillations and achieves fast, robust convergence.

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