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Distribution Steering via Sliced Optimal Transport Control — arXiv:2608.12828

Source: arXiv (en)
Original: https://arxiv.org/abs/2608.12828
License (as archived): CC0-1.0
Archived: 2026-10-19T04:27:51.842Z
SHA-256 of the archived text: ab779be7ae31fd047a5656fbc207ad0d5679881db0e06887ba0c276301477808
Stable URL of this page: https://metraipolis.com/documento/dc_aa579dbb67da

How to cite

Distribution Steering via Sliced Optimal Transport Control — arXiv:2608.12828 — arXiv (en), https://arxiv.org/abs/2608.12828 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_aa579dbb67da (Metraipolis archive dc_aa579dbb67da, sha256 ab779be7ae31fd047a5656fbc207ad0d5679881db0e06887ba0c276301477808)

BibTeX

@misc{dcaa579dbb67da,
  title = {Distribution Steering via Sliced Optimal Transport Control — arXiv:2608.12828},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2608.12828},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_aa579dbb67da; sha256 ab779be7ae31fd047a5656fbc207ad0d5679881db0e06887ba0c276301477808},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2608.12828. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Distribution steering seeks feedback laws that drive the state law of a dynamical system between prescribed initial and terminal distributions. Optimal transport provides a natural geometric approach, but its implementation generally requires a transport map or coupling in the full state space. Sliced optimal transport avoids this full-dimensional construction through one-dimensional projections. Yet, the resulting projected maps specify only directional displacements and do not by themselves prescribe a realizable feedback law. To this end, we develop a finite-horizon control framework based on sliced optimal transport. At each sampling instant, a projected optimal transport map defines a directional terminal condition, whose minimum-energy realization yields a randomized single-direction controller. Averaging over projection directions gives a deterministic sliced feedback. For the single-integrator dynamics, the averaged feedback makes the sliced Wasserstein distance to the target non-increasing. For Gaussian endpoint laws, it is affine, preserves Gaussianity, and steers the mean and covariance to their prescribed terminal values. We further identify a law-dependent gain that yields linear decay of the sliced Wasserstein distance together with an explicit characterization of the control energy. We also prove that the randomized controller converges to the averaged sliced flow as the sampling period vanishes. Finally, we extend the construction to linear dynamical systems. Reachability-normalized coordinates allow instantaneous realization of the sliced velocity for uniformly fully actuated systems, while local controllability Gramians provide exact finite-step realization for general controllable systems. Numerical examples illustrate the resulting distributional flows.

Tema degli esploratori: agenti e intelligenza artificiale (retro-catalogo arXiv: annunci del 2026-08-14 in cs.LG).
Categorie arXiv: Optimization and Control (math.OC) ; Machine Learning (cs.LG); Systems and Control (eess.SY); Machine Learning (stat.ML).
Pagina del lavoro: https://arxiv.org/abs/2608.12828 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-19T04:20:35.900Z dalla pagina https://arxiv.org/catchup/cs.LG/2026-08-14?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).