发表机构
Laboratoire des Signaux et Systèmes, CentraleSupélec; School of Mathematics, University of Bristol（信号与系统实验室，中央苏佩莱克学院; 布里斯托大学数学学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究双矩阵两人博弈中乐观指数权重方法迭代的收敛与稳定性，允许步长非对称。给出零和博弈全局最后迭代收敛充分条件及一般双矩阵博弈渐近稳定性和不稳定性阈值，推导特殊情况结果并实验验证。
AI 中文摘要
我们研究双矩阵两人博弈，并研究乐观指数权重方法生成的迭代的最后迭代收敛性和均衡稳定性。与先前工作不同，我们允许步长$\eta_x$和$\eta_y$不同。我们的第一个主要结果在不动点集有限的假设下，为零和博弈的特殊情况建立了全局最后迭代收敛的充分条件，该条件仅约束步长的乘积$\eta_x\eta_y$。此条件具有实际相关性并部分解释了经验观察到的行为。我们的第二个主要结果为一般双矩阵博弈的渐近稳定性和不稳定性提供了一个几乎紧密的阈值，同样是根据步长的乘积。该结果主要具有理论意义。我们推导了特殊情况下的几个已知结果和实际相关的步长界限，并通过实验说明了我们的结果。
英文摘要
We study bimatrix two-player games and investigate the last-iterate convergence and stability of equilibria for the iterates generated by the optimistic exponential weights method. In contrast to prior work, we allow the step sizes $η_x$ and $η_y$ to differ. Our first main result establishes, under the assumption that the set of fixed points is finite, a sufficient condition for global last-iterate convergence in the special case of zero-sum games, which constrains only the product $η_xη_y$ of the step sizes. This condition is practically relevant and partially explains empirically observed behavior. Our second main result provides an almost-tight threshold for asymptotic stability and instability, again in terms of products of the step sizes, for general bimatrix games. This result is primarily of theoretical interest. We derive several known results and practically relevant step size bounds for special cases and illustrate our results by experiments.
