# Enhanced Adaptive Gradient Algorithms for Nonconvex-PL Minimax Optimization Source: [Enhanced Adaptive Gradient Algorithms for Nonconvex-PL Minimax Optimization]() Collection index: [llms.txt]() Data updated: 2025-10-25T18:11:08.239Z Authors: Feihu Huang, Chunyu Xuan, Xinrui Wang, Siqi Zhang, Songcan Chen Published: 2023-03-07T15:33:12.000Z ## Abstract Minimax optimization recently is widely applied in many machine learning tasks such as generative adversarial networks, robust learning and reinforcement learning. In the paper, we study a class of nonconvex-nonconcave minimax optimization with nonsmooth regularization, where the objective function is possibly nonconvex on primal variable $x$, and it is nonconcave and satisfies the Polyak-Lojasiewicz (PL) condition on dual variable $y$. Moreover, we propose a class of enhanced momentum-based gradient descent ascent methods (i.e., MSGDA and AdaMSGDA) to solve these stochastic nonconvex-PL minimax problems. In particular, our AdaMSGDA algorithm can use various adaptive learning rates in updating the variables $x$ and $y$ without relying on any specifical types. Theoretically, we prove that our methods have the best known sample complexity of $\\tilde{O}(\\epsilon^{-3})$ only requiring one sample at each loop in finding an $\\epsilon$-stationary solution. Some numerical experiments on PL-game and Wasserstein-GAN demonstrate the efficiency of our proposed methods. ## Recorded benchmark results A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage. - [Stochastic Minimax Optimization on Theoretical Analysis](): Stochastic Minimax Optimization; Theoretical Analysis; Sample Complexity: -3. ## Original sources and implementation [Original paper]() [PDF]()