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

2025-08-08

AI Summary

This work addresses the data-driven chance-constrained density control problem: steering the probability density evolution of a system with unknown linear autoregressive dynamics, Gaussian mixture initial state distribution, and a terminal state distribution required to match a prescribed Gaussian target. Methodologically, we innovatively introduce the Gromov–Wasserstein (GW) optimal transport distance into this setting—leveraging input–output trajectory data to implicitly encode the unknown dynamics without explicit system identification. We formulate a density-matching objective measured by the GW distance and equivalently recast the original nonconvex optimization into a tractable difference-of-convex (DC) program. Numerical experiments demonstrate that the proposed approach achieves high-precision terminal density matching across diverse data regimes, significantly enhancing both feasibility and robustness of stochastic constrained density control under unknown dynamics.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Mixed Discrete/Continuous Search
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Data management and stream processing for Web, mobile and wireless applications
• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work

Abstract

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.

Problem

• Data-driven chance-constrained density steering problem
• Unknown linear controlled recursion dynamics
• Optimal control reformulated as convex program

Innovation

• Uses Gromov-Wasserstein metric for density steering
• Reformulates problem as difference-of-convex program
• Solves efficiently via DC algorithm