论文标题
对于平均场二人游戏零和游戏，可证明是收敛的绝对动力学
Provably convergent quasistatic dynamics for mean-field two-player zero-sum games
论文作者
论文摘要
在本文中，我们研究了为平均场两人零和游戏寻找混合NASH平衡的问题。解决此问题需要优化两个概率分布。我们考虑了一个准危机的瓦斯汀梯度流动动力学，其中一个概率分布遵循Wasserstein梯度流动，而另一个始终处于平衡状态。理论分析是对这种动力学进行的，表明其在轻度条件下的混合NASH平衡。受概率分布的连续动力学的启发，我们得出了带有内在迭代的绝对langevin梯度下降方法，并在不同问题上测试该方法，包括gan的训练混合物。
In this paper, we study the problem of finding mixed Nash equilibrium for mean-field two-player zero-sum games. Solving this problem requires optimizing over two probability distributions. We consider a quasistatic Wasserstein gradient flow dynamics in which one probability distribution follows the Wasserstein gradient flow, while the other one is always at the equilibrium. Theoretical analysis are conducted on this dynamics, showing its convergence to the mixed Nash equilibrium under mild conditions. Inspired by the continuous dynamics of probability distributions, we derive a quasistatic Langevin gradient descent method with inner-outer iterations, and test the method on different problems, including training mixture of GANs.
