Moment Constrained Optimal Transport for Control Applications
Thomas Le Corre, Ana Busic, Sean Meyn
TL;DR
This paper introduces a moment constrained optimal transport method for control applications, enabling agent coordination without predefined target distributions, with computational solutions and real-world electric vehicle charging case studies.
Contribution
It proposes a novel moment constrained OT relaxation for control, incorporating entropic regularization and a Sinkhorn-inspired algorithm for distributed control.
Findings
Effective in coordinating EV charging while respecting grid constraints
Demonstrated scalability with 10,000 transactions in case study
Outperforms traditional methods in flexibility and constraint satisfaction
Abstract
This paper concerns the application of techniques from optimal transport (OT) to mean field control, in which the probability measures of interest in OT correspond to empirical distributions associated with a large collection of controlled agents. The control objective of interest motivates a one-sided relaxation of OT, in which the first marginal is fixed and the second marginal is constrained to a moment class: a set of probability measures defined by generalized moment constraints. This relaxation is particularly interesting for control problems as it enables the coordination of agents without the need to know the desired distribution beforehand. The inclusion of an entropic regularizer is motivated by both computational considerations, and also to impose hard constraints on agent behavior. A computational approach inspired by the Sinkhorn algorithm is proposed to solve this problem.…
Peer Reviews
Decision·Submitted to ICLR 2025
- The problem being considered is an interesting one. - The idea of controlling an distribution to look like another (more optimal) distribution is certainly useful.
It's important to note that I'm not that familiar with the field of optimal transport. But I felt the following are the weaknesses: - The abstract, intro conclusion seem to promise a lot more than what the math actually delivers? The algorithm relies on Gibbs kernels, which feels pretty standard. How broadly applicable is this? - The EV problem presented is somewhat strange. The paper seems to say that the controllable variables are the EV arrival time and state-of-charge? But these are typical
The EV Charging problem has received much attention recently. This work aims to optimize the consumption while satisfying the grid constraints.
The theoretical part of this paper is hard for me to follow. The introduction starts with the mathematical problem settings without sufficient discussion about the background, significant challenges, and the motivation for using optimal transport in mean-field control. Besides, the theoretical problem setting, assumptions, and propositions are difficult to interpret. I suggest the authors add more discussions about the connections between the general framework and a specific example (e.g., the E
The approach of leveraging computational techniques from optimal control theory for control problems and the observations obtained from experiments applying the approach can be interesting. They provide the background theoretical derivation of such an approach. The approach focuses on a finite set of moments, so it could be more tractable in practice.
**Writing:** The reviewer thinks the writing of this paper needs to be improved. The reviewer was confused by the abstract and couldn't understand what contributions were made in this paper at first. The authors barely use phrases like 'this paper' or 'we,' so the actions taken in the paper were not distinguished clearly. It seems this issue occurs throughout the paper as well. The reviewer feels that the authors didn't clearly articulate the prior approaches, what they did new, and what the adv
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Taxonomy
TopicsGroundwater flow and contamination studies · Markov Chains and Monte Carlo Methods · Probabilistic and Robust Engineering Design