论文标题
非滑动非Convex-Nonconcave Min-Max问题和生成对抗网络的最佳条件
Optimality conditions for nonsmooth nonconvex-nonconcave min-max problems and generative adversarial networks
论文作者
论文摘要
本文考虑了机器学习和游戏中的一类非平滑性非Convex-Nonconcave Min-Max问题。我们首先为存在全球最小点和局部minimax点的存在提供了足够的条件。接下来，我们通过使用定向衍生物为局部最小值点建立了一阶和二阶最佳条件。这些条件减少了fr {é} chet衍生物的平滑最大最大问题。我们将理论结果应用于生成的对抗网络（GAN），其中两个神经网络在游戏中相互竞争。示例用于说明新理论在培训gan中的应用。
This paper considers a class of nonsmooth nonconvex-nonconcave min-max problems in machine learning and games. We first provide sufficient conditions for the existence of global minimax points and local minimax points. Next, we establish the first-order and second-order optimality conditions for local minimax points by using directional derivatives. These conditions reduce to smooth min-max problems with Fr{é}chet derivatives. We apply our theoretical results to generative adversarial networks (GANs) in which two neural networks contest with each other in a game. Examples are used to illustrate applications of the new theory for training GANs.
