论文标题
在潜在的平均野外游戏中的通用条件梯度和学习
Generalized conditional gradient and learning in potential mean field games
论文作者
论文摘要
我们研究了二阶，潜在和单调的平均野外游戏的分辨率，该局部比赛是富有条件的梯度算法的分辨率，这是Frank-Wolfe算法的扩展。我们表明该方法等同于虚拟的游戏方法。我们建立了最佳差距，可利用性和变量与均值野外游戏唯一解决方案的距离的收敛速率，以实现各种步骤。特别是，我们表明，当lineSearch计算得出步骤时，可以实现线性收敛。
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.
