Motivated by recent advances in both theoretical and applied aspects of multiplayer games, spanning from e-sports to multi-agent generative adversarial networks, we focus on min-max optimization in team zero-sum games. In this class of games, players are split in two teams with payoffs equal within the same team and of opposite sign across the opponent team. Unlike the textbook two-player zero-sum games, finding a Nash equilibrium in our class can be shown to be CLS-hard, i.e., it is unlikely to have a polynomial time algorithm for computing Nash equilibria. Moreover in this generalized framework, we establish that even asymptotic last iterate or time average convergence to a Nash Equilibrium is not possible using Gradient Descent Ascent (GDA), its optimistic variant and extra gradient. Specifically, we present a family of team games whose induced utility is \emph{non} multi-linear with \emph{non} attractive \emph{per-se} mixed Nash Equilibria, as strict saddle points of the underlying optimization landscape. Leveraging techniques from control theory, we complement these negative results by designing a modified GDA that converges locally to Nash equilibria. Finally, we discuss connections of our framework with AI architectures with team competition structure like multi-agent generative adversarial networks.

研究内容涵盖电子竞技中的机器学习，多代理生成对抗网络的表现力，以及两队博弈中的优化问题和Nash均衡解的解决方案。通过考虑全信息反馈下的游戏，对在线学习算法的能力进行了讨论，并提出了一个基于控制论技术的一阶方法用于解决该类问题，该方法能够在某些条件下享有局部收敛性。

在两队零和博弈中收敛到纳什均衡