Schrodinger Bridges and Density Steering Problems for Gaussian Mixtures Models in Discrete-Time
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866908931512598528 |
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| author | Rapakoulias, George Liu, Fengjiao Tsiotras, Panagiotis |
| author_facet | Rapakoulias, George Liu, Fengjiao Tsiotras, Panagiotis |
| contents | In this work, we revisit the discrete-time Schrödinger Bridge (SB) and Density Steering (DS) problems for Gaussian mixture model (GMM) boundary distributions. Building on the existing literature, we construct a set of feasible Markovian policies that transport the initial distribution to the final distribution, and are expressed as mixtures of elementary component-to-component optimal policies. We then study the policy optimization within this feasible set in the context of discrete-time SBs and density-steering problems, respectively. We show that for minimum-effort density-steering problems, the proposed policy achieves the same control cost as existing approaches in the literature. For discrete-time SB problems, the proposed policy yields a cost smaller than or equal to that in the literature, resulting in a less conservative approximation. Finally, we study the continuous-time limit of our proposed discrete-time approach and show that it agrees with recently proposed approximations to the continuous-time SB for GMM boundary distributions. We illustrate this new result through two numerical examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_01144 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Schrodinger Bridges and Density Steering Problems for Gaussian Mixtures Models in Discrete-Time Rapakoulias, George Liu, Fengjiao Tsiotras, Panagiotis Systems and Control In this work, we revisit the discrete-time Schrödinger Bridge (SB) and Density Steering (DS) problems for Gaussian mixture model (GMM) boundary distributions. Building on the existing literature, we construct a set of feasible Markovian policies that transport the initial distribution to the final distribution, and are expressed as mixtures of elementary component-to-component optimal policies. We then study the policy optimization within this feasible set in the context of discrete-time SBs and density-steering problems, respectively. We show that for minimum-effort density-steering problems, the proposed policy achieves the same control cost as existing approaches in the literature. For discrete-time SB problems, the proposed policy yields a cost smaller than or equal to that in the literature, resulting in a less conservative approximation. Finally, we study the continuous-time limit of our proposed discrete-time approach and show that it agrees with recently proposed approximations to the continuous-time SB for GMM boundary distributions. We illustrate this new result through two numerical examples. |
| title | Schrodinger Bridges and Density Steering Problems for Gaussian Mixtures Models in Discrete-Time |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2604.01144 |