平均场博弈中的学习控制：虚拟博弈与相关梯度下降
Learning controls in mean field games: the fictitious play and related gradient descent
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中文总结 AI 辅助
本文研究势平均场博弈中两种学习过程：基于控制更新的虚拟博弈和主代理的梯度下降，均证明在一般条件下收敛到均衡解。
中文摘要 AI 辅助
我们研究了两种学习过程及其与势平均场博弈（MFG）中均衡形成的关系。第一种是虚拟博弈的一个版本，其中玩家直接观察其他玩家的行动（控制），并通过关于控制的更新规则学习MFG的分布。这导致了一种新的迭代过程，该过程对于一大类势MFG控制问题收敛，即使在存在共同噪声的情况下也是如此。另一方面，我们还考虑了主代理的学习过程，该代理试图仅利用局部梯度信息来解决平均场控制问题。我们证明，在非常一般的假设下，该代理的梯度下降收敛到相关势MFG的解。
英文摘要
We investigate two learning procedures and their relationship to the formation of equilibrium in potential mean field games (MFGs). The first one is a version of the fictitious play in which players observe directly the actions (controls) of other players and learn the distribution of the MFG through an update rules on controls. This leads to a new iterative procedure which converges for a wide class of potential MFGs of controls, even in the presence of common noise. On the other hand we also consider the learning procedure of a principal agent trying to solve a mean field control problem with only local gradient information. We prove that under very general assumption, the gradient descent of such agent converges to a solution of the associated potential MFG.
