Machine-Learned Sampling of Conditioned Path Measures

Track: Main Track

Keywords: Path Measure Sampling, Controlled Equilibrium Dynamics, Wasserstein Gradient Flow, Regularized Optimal Transport

Abstract: We propose algorithms for sampling from posterior path measures $\mathcal{P}(\mathcal{C}([0, T], \mathbb{R}^d))$ under a general prior process. This leverages ideas from (1) controlled equilibrium dynamics, which gradually transport between two path measures, (2) optimization in $\infty$-dimensional probability space endowed with a Wasserstein metric, which can be used to evolve a density curve under the specified likelihood. The resulting algorithms are theoretically grounded and can be integrated seamlessly with neural networks for learning the target trajectory ensembles, without access to data.

Submission Number: 47