论文标题
连续游戏中梯度学习动态的稳定性：标量动作空间
Stability of Gradient Learning Dynamics in Continuous Games: Scalar Action Spaces
论文作者
论文摘要
游戏中的学习过程解释了玩家如何在寻求平衡时互相努力。我们根据两人连续游戏中的个体渐变学习自然学习模型。在这样的游戏中，可以说是局部平衡的自然概念是差异的纳什平衡。但是，学习动力学的一组本地稳定的平衡不一定与相应游戏的一组差异nash平衡相吻合。为了表征这一差距，我们通过利用线性化游戏动力学的频谱来为这种固定点的稳定性或不稳定提供正式的保证。我们对标量游戏提供了全面的了解，并发现既稳定又纳什的平衡对于学习率的变化是有力的。
Learning processes in games explain how players grapple with one another in seeking an equilibrium. We study a natural model of learning based on individual gradients in two-player continuous games. In such games, the arguably natural notion of a local equilibrium is a differential Nash equilibrium. However, the set of locally exponentially stable equilibria of the learning dynamics do not necessarily coincide with the set of differential Nash equilibria of the corresponding game. To characterize this gap, we provide formal guarantees for the stability or instability of such fixed points by leveraging the spectrum of the linearized game dynamics. We provide a comprehensive understanding of scalar games and find that equilibria that are both stable and Nash are robust to variations in learning rates.
