论文标题
连续游戏中梯度学习动态的稳定性：向量动作空间
Stability of Gradient Learning Dynamics in Continuous Games: Vector Action Spaces
论文作者
论文摘要
为了表征游戏的优化景观，本文分析了在两人连续游戏的固定点附近基于梯度的动力学的稳定性。我们介绍了二次数值范围，作为一种表征游戏动力学频谱的方法，并证明了平衡对学习率的变化的鲁棒性。通过将游戏分解为对称和偏斜的成分，我们评估了向量场的潜力和旋转成分对差异NASH平衡稳定性的贡献。我们的结果表明，在零和游戏中，所有NASH都稳定且稳健。在潜在的游戏中，所有稳定的积分都是纳什。对于通用游戏，我们为不稳定性提供了足够的条件。我们以一个数字示例结束，其中学习时间尺度分离会导致更快的收敛性。
Towards characterizing the optimization landscape of games, this paper analyzes the stability of gradient-based dynamics near fixed points of two-player continuous games. We introduce the quadratic numerical range as a method to characterize the spectrum of game dynamics and prove the robustness of equilibria to variations in learning rates. By decomposing the game Jacobian into symmetric and skew-symmetric components, we assess the contribution of a vector field's potential and rotational components to the stability of differential Nash equilibria. Our results show that in zero-sum games, all Nash are stable and robust; in potential games, all stable points are Nash. For general-sum games, we provide a sufficient condition for instability. We conclude with a numerical example in which learning with timescale separation results in faster convergence.
