Dynamic Programming in Probability Spaces via Optimal Transport
Optimization and Control
2024-04-09 v2 Systems and Control
Systems and Control
Abstract
We study discrete-time finite-horizon optimal control problems in probability spaces, whereby the state of the system is a probability measure. We show that, in many instances, the solution of dynamic programming in probability spaces results from two ingredients: (i) the solution of dynamic programming in the "ground space" (i.e., the space on which the probability measures live) and (ii) the solution of an optimal transport problem. From a multi-agent control perspective, a separation principle holds: The "low-level control of the agents of the fleet" (how does one reach the destination?) and "fleet-level control" (who goes where?) are decoupled.
Cite
@article{arxiv.2302.13550,
title = {Dynamic Programming in Probability Spaces via Optimal Transport},
author = {Antonio Terpin and Nicolas Lanzetti and Florian Dörfler},
journal= {arXiv preprint arXiv:2302.13550},
year = {2024}
}