Learning Paths for Dynamic Measure Transport: A Control Perspective
Aimee Maurais, Bamdad Hosseini, Youssef Marzouk
我们为通过动态测量传输(DMT)确定采样措施路径的问题带来了控制视角。 我们强调这样一个事实,即常用的路径可能是DMT的糟糕选择,并将学习替代路径的现有方法与平均场游戏联系起来。 基于这些连接,我们提出了一个灵活的优化问题家族,用于确定DMT措施的倾斜路径,并倡导使用鼓励相应速度平滑的客观术语。 我们提出了一个基于最近高斯过程方法解决这些问题的数值算法,用于解决偏微分方程,并展示了与使用直到参考路径的方法相比,我们的方法恢复更有效和平滑的传输模型的能力。
We bring a control perspective to the problem of identifying paths of measures for sampling via dynamic measure transport (DMT). We highlight the fact that commonly used paths may be poor choices for DMT and connect existing methods for learning alternate paths to mean-field games. Based on these connections we pose a flexible family of optimization problems for identifying tilted paths of measures for DMT and advocate for the use of objective terms which encourage smoothness of the correspondin...