Learning Paths for Dynamic Measure Transport: A Control Perspective
This work addresses sampling efficiency in computational statistics, though it appears incremental as it builds on existing DMT and mean-field game connections.
The paper tackles the problem of identifying optimal measure paths for dynamic measure transport (DMT) sampling by proposing a control-based approach that learns tilted paths with smooth velocities, resulting in more efficient and smooth transport models compared to standard untilted paths.
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.