Alternating gradient-descent-ascent (AltGDA) is an optimization algorithm that has been widely used for model training in various machine learning applications, which aim to solve a nonconvex minimax optimization problem. However, the existing studies show that it suffers from a high computation complexity in nonconvex minimax optimization. In this paper, we develop a single-loop and fast AltGDA-type algorithm that leverages proximal gradient updates and momentum acceleration to solve regularized nonconvex minimax optimization problems. By identifying the intrinsic Lyapunov function of this algorithm, we prove that it converges to a critical point of the nonconvex minimax optimization problem and achieves a computation complexity $\mathcal{O}(\kappa^{1.5}\epsilon^{-2})$, where $\epsilon$ is the desired level of accuracy and $\kappa$ is the problem's condition number. Such a computation complexity improves the state-of-the-art complexities of single-loop GDA and AltGDA algorithms (see the summary of comparison in Table 1). We demonstrate the effectiveness of our algorithm via an experiment on adversarial deep learning.

翻译：在各种机器学习应用程序的模型培训中,人们广泛使用一种优化算法(AltGDA),这种算法旨在解决非convex小型最大最大优化问题,但是,现有的研究表明,在非convex微型最大优化中,这种算法具有很高的计算复杂性。在本文中,我们开发了一种单环和快速的 AltGDA 型算法,利用近似梯度更新和加速力来解决正常化的非convelx小型最大优化问题。通过确定这一算法的固有Lyapunov功能,我们证明它与非convex小型最大优化问题的关键点相融合,并实现了一个计算复杂性$\mathcal{O}(\ kapapa ⁇ 1.5 ⁇ epsilon ⁇ -2}) $(kapsilon是理想的准确度,而$\kappa美元是问题的条件号。这样的计算复杂性提高了该算法的状态-艺术复杂性。我们通过深入的对比性分析,展示了我们通过演算法的测试的有效性。