We investigate the resolution of second-order, potential, and monotone mean field games with the generalized conditional gradient algorithm, an extension of the Frank-Wolfe algorithm. We show that the method is equivalent to the fictitious play method. We establish rates of convergence for the optimality gap, the exploitability, and the distances of the variables to the unique solution of the mean field game, for various choices of stepsizes. In particular, we show that linear convergence can be achieved when the stepsizes are computed by linesearch.

中文翻译：

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势平均场博弈中的广义条件梯度和学习

我们使用广义条件梯度算法（Frank-Wolfe 算法的扩展）研究二阶势单调平均场博弈的分辨率。我们证明该方法与虚拟游戏方法等效。对于各种步长选择，我们建立了最优差距、可利用性以及变量到平均场博弈唯一解的距离的收敛率。特别是，我们表明当通过线性搜索计算步长时可以实现线性收敛。