Controlled-Minimax: Stabilizing Adversarial Optimization via Control Theory
Minimax optimization is fundamental to adversarial learning yet suffers from severe stability challenges, often manifesting as persistent limit cycles or divergence. This paper investigates these instabilities through the lens of continuous-time dynamical systems. By modeling training dynamics as a second-order Ordinary Differential Equation (ODE), we rigorously identify the root cause of non-convergence: the problematic eigenstructure of the loss function's Hessian near equilibrium points. To address this, we introduce Controlled-Minimax, a novel stabilization framework that reformulates the optimization trajectory as a controllable physical system. Unlike heuristic regularization techni...
| Authors | Tianjiao Luo, Jianfei Chen, Jun Zhu |
|---|---|
| Primary category | cs.LG |
| Published | 9 October 2026 |
| Last updated at source | 9 October 2026 |
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