论文标题
高维非本地均值游戏的随机功能
Random Features for High-Dimensional Nonlocal Mean-Field Games
论文作者
论文摘要
我们提出了一种有效的解决方案方法，用于基于通过随机特征的相互作用内核的蒙特卡洛近似的高维非本地平均场游戏（MFG）系统。我们通过传递功能空间来避免在状态空间中交互作用项的昂贵空间散布。这种方法允许几乎任何单一轨迹优化算法的无缝平均场扩展。在这里，我们将最佳控制中的直接转录方法扩展到平均场设置。我们通过解决高维空间中的MFG问题来证明我们方法的效率，这些空间以前对常规的非深度学习技术遥不可及。
We propose an efficient solution approach for high-dimensional nonlocal mean-field game (MFG) systems based on the Monte Carlo approximation of interaction kernels via random features. We avoid costly space-discretizations of interaction terms in the state-space by passing to the feature-space. This approach allows for a seamless mean-field extension of virtually any single-agent trajectory optimization algorithm. Here, we extend the direct transcription approach in optimal control to the mean-field setting. We demonstrate the efficiency of our method by solving MFG problems in high-dimensional spaces which were previously out of reach for conventional non-deep-learning techniques.
