论文标题
平均现场游戏反问题
A mean field game inverse problem
论文作者
论文摘要
平均场游戏在包括经济学，工程和机器学习在内的各个领域中出现。他们研究了个人通过某些平均场数量相互作用的大量人群中的战略决策。游戏的地面指标和运行成本至关重要，但通常是未知或仅部分知道的。在本文中，我们建议在运行成本中重建地面指标和互动内核。观察结果是特异性的宏观运动，即密度分布和速度场。它们在某种程度上可能会因噪音而破坏。我们的模型是PDE受约束的优化问题，可以通过一阶原始偶对偶方法解决。此外，我们应用Bregman迭代以找到最佳模型参数。我们从数值上证明了我们的模型既有效又适合噪声。
Mean-field games arise in various fields including economics, engineering, and machine learning. They study strategic decision making in large populations where the individuals interact via certain mean-field quantities. The ground metrics and running costs of the games are of essential importance but are often unknown or only partially known. In this paper, we propose mean-field game inverse-problem models to reconstruct the ground metrics and interaction kernels in the running costs. The observations are the macro motions, to be specific, the density distribution, and the velocity field of the agents. They can be corrupted by noise to some extent. Our models are PDE constrained optimization problems, which are solvable by first-order primal-dual methods. Besides, we apply Bregman iterations to find the optimal model parameters. We numerically demonstrate that our model is both efficient and robust to noise.
