从控制视角优化测度传输路径，提升采样效率与平滑性。
Learning Paths for Dynamic Measure Transport: A Control Perspective
- 基于控制理论构建可调路径优化框架
- 新方法生成更平滑高效的测度传输路径
- 适合需要高质量采样轨迹的研究者
我们将控制论视角引入动态测度传输（DMT）中的测度路径识别问题。指出常用路径在DMT中表现不佳，并将现有学习替代路径的方法与平均场博弈联系起来。基于此，提出一个灵活的优化问题族，用于寻找适用于DMT的倾斜测度路径，并倡导使用促进对应速度平滑性的目标项。我们提出一种基于最新高斯过程求解偏微分方程的方法的数值算法，并展示了该方法相比未倾斜参考路径能恢复出更高效、更平滑的传输模型。
原文摘要 · Abstract (English)
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 corresponding velocities. We present a numerical algorithm for solving these problems based on recent Gaussian process methods for solution of partial differential equations and demonstrate the ability of our method to recover more efficient and smooth transport models compared to those which use an untilted reference path.
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