# Data-Driven Density Steering via the Gromov-Wasserstein Optimal Transport Distance

arXiv: https://arxiv.org/abs/2508.06052 · HTML: https://mlsanity.com/paper/2508.06052/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 20 references that are in the map.
- First posted on arXiv 8 Aug 2025.

## Builds on (most cited first, 11 of 11)

- [Formulas for Data-driven Control: Stabilization, Optimality and Robustness](https://mlsanity.com/paper/1903.06842/) (2019)
- [Belief Space Planning: A Covariance Steering Approach](https://mlsanity.com/paper/2105.11092/) (2021)
- [Minimum energy density steering of linear systems with Gromov-Wasserstein terminal cost](https://mlsanity.com/paper/2402.15942/) (2024)
- [Computationally Efficient Covariance Steering for Systems Subject to Parametric Disturbances and Chance Constraints](https://mlsanity.com/paper/2301.07308/) (2023)
- [Density Steering of Gaussian Mixture Models for Discrete-Time Linear Systems](https://mlsanity.com/paper/2311.08500/) (2023)
- [Chance-Constrained Gaussian Mixture Steering to a Terminal Gaussian Distribution](https://mlsanity.com/paper/2403.16302/) (2024)
- [Formation Shape Control using the Gromov-Wasserstein Metric](https://mlsanity.com/paper/2503.21538/) (2025)
- [Covariance Steering for Systems Subject to Unknown Parameters](https://mlsanity.com/paper/2303.10293/) (2023)
- [Data-Driven Covariance Steering Control Design](https://mlsanity.com/paper/2303.17675/) (2023)
- [Data-Driven Robust Covariance Control for Uncertain Linear Systems](https://mlsanity.com/paper/2312.05833/) (2023)
- [Stochastic Control of UAVs: An Optimal Tradeoff between Performance, Flight Smoothness and Control Effort](https://mlsanity.com/paper/2409.10369/) (2024)

## Abstract (arXiv)

We tackle the data-driven chance-constrained density steering problem using the Gromov-Wasserstein metric. The underlying dynamical system is an unknown linear controlled recursion, with the assumption that sufficiently rich input-output data from pre-operational experiments are available. The initial state is modeled as a Gaussian mixture, while the terminal state is required to match a specified Gaussian distribution. We reformulate the resulting optimal control problem as a difference-of-convex program and show that it can be efficiently and tractably solved using the DC algorithm. Numerical results validate our approach through various data-driven schemes.