非凸Min-Max Optimization：应用、挑战和最新理论进展
Non-convex Min-Max Optimization: Applications, Challenges, and Recent Theoretical Advances
摘要：
最小-最大最优化问题，也被称为鞍点问题，是一个经典的最优化问题，它也被研究在零和对策的背景下。给定一类目标函数，目标是找到一个值的参数，导致一个小的目标值，即使是最坏的情况下的功能在给定的类。最近，最小-最大最优化问题在广泛的信号和数据处理应用中变得非常流行，例如公平波束成形、训练生成对抗网络（GANs）和鲁棒机器学习等。这篇文章的总体目标是提供一个调查的最小化和最大化问题的一个重要子类的最新进展，其中的最小化和最大化问题可以是非凸和/或非凹的。特别是，我们将首先提出一些应用程序来展示这种最小最大问题的重要性，然后我们讨论关键的理论挑战，并提供一些令人兴奋的最近的理论和算法的进展，在解决非凸最小最大问题的选择性审查。最后，我们将指出开放的问题和未来的研究方向。
英文摘要：
The min-max optimization problem, also known as the saddle point problem, is a classical optimization problem which is also studied in the context of zero-sum games. Given a class of objective functions, the goal is to find a value for the argument which leads to a small objective value even for the worst case function in the given class. Min-max optimization problems have recently become very popular in a wide range of signal and data processing applications such as fair beamforming, training generative adversarial networks (GANs), and robust machine learning, to just name a few. The overarching goal of this article is to provide a survey of recent advances for an important subclass of min-max problem, where the minimization and maximization problems can be non-convex and/or non-concave. In particular, we will first present a number of applications to showcase the importance of such min-max problems; then we discuss key theoretical challenges, and provide a selective review of some exciting recent theoretical and algorithmic advances in tackling non-convex min-max problems. Finally, we will point out open questions and future research directions.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
