研究双时间尺度梯度上升下降法的收敛性，揭示学习率比例的关键作用。
Convergence of two-timescale gradient descent ascent dynamics: finite-dimensional and mean-field perspectives
- 通过拟静态分析与混合耦合技术，构建收敛理论框架。
- 在有限维和平均场设置下，证明了学习率比例影响收敛结果。
- 适合优化、博弈论与强化学习研究者参考。
双时间尺度梯度下降-上升（GDA）是用于寻找极小极大博弈中纳什均衡的经典算法。本文从有限维与平均场两个角度，分析学习率比例对收敛行为的影响。对于有限维二次极小极大博弈，采用超协稳性方法，在近拟静态情形下获得长期收敛性。对于平均场GDA动力学，利用混合同步-反射耦合技术，在有限尺度比条件下研究收敛性。
原文摘要 · Abstract (English)
The two-timescale gradient descent-ascent (GDA) is a canonical gradient algorithm designed to find Nash equilibria in min-max games. We analyze the two-timescale GDA by investigating the effects of learning rate ratios on convergence behavior in both finite-dimensional and mean-field settings. In particular, for finite-dimensional quadratic min-max games, we obtain long-time convergence in near quasi-static regimes through the hypocoercivity method. For mean-field GDA dynamics, we investigate convergence under a finite-scale ratio using a mixed synchronous-reflection coupling technique.
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