Enhanced Adaptive Gradient Algorithms for Nonconvex-PL Minimax Optimization
This work addresses minimax optimization problems in machine learning tasks like GANs and robust learning, offering incremental improvements in algorithm efficiency for this specific domain.
The authors tackled the problem of nonconvex-PL minimax optimization with nonsmooth regularization, proposing enhanced momentum-based gradient descent ascent methods (MSGDA and AdaMSGDA) that achieve a sample complexity of $ ilde{O}(ε^{-3})$ for finding an $ε$-stationary solution, as demonstrated in experiments on PL-game and Wasserstein-GAN.
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 $\tilde{O}(ε^{-3})$ only requiring one sample at each loop in finding an $ε$-stationary solution. Some numerical experiments on PL-game and Wasserstein-GAN demonstrate the efficiency of our proposed methods.