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Quantitative Target Convergence and Uniform-in-Time Propagation of Chaos for Langevin-Regularized SVGD — arXiv:2608.28827

Source: arXiv (en)
Original: https://arxiv.org/abs/2608.28827
License (as archived): CC0-1.0
Archived: 2026-10-17T08:39:40.596Z
SHA-256 of the archived text: 5810f1a916b79f6a5a2f318fa448f257587c44607c6e605e21b8c081cb14275b
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How to cite

Quantitative Target Convergence and Uniform-in-Time Propagation of Chaos for Langevin-Regularized SVGD — arXiv:2608.28827 — arXiv (en), https://arxiv.org/abs/2608.28827 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_7a40320d52fb (Metraipolis archive dc_7a40320d52fb, sha256 5810f1a916b79f6a5a2f318fa448f257587c44607c6e605e21b8c081cb14275b)

BibTeX

@misc{dc7a40320d52fb,
  title = {Quantitative Target Convergence and Uniform-in-Time Propagation of Chaos for Langevin-Regularized SVGD — arXiv:2608.28827},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2608.28827},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_7a40320d52fb; sha256 5810f1a916b79f6a5a2f318fa448f257587c44607c6e605e21b8c081cb14275b},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2608.28827. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We establish quantitative convergence to the target and uniform-in-time propagation of chaos for Langevin-regularized Stein variational gradient descent. The Stein interaction need not be small relative to the confining Langevin drift and does not generally yield a contractive particle coupling. At the mean-field level, the Stein and Langevin components dissipate the same relative entropy in the kernel-induced Stein and $2$-Wasserstein geometries, producing the squared kernel Stein discrepancy and relative Fisher information. Under a log-Sobolev inequality for the target, this yields exponential last-iterate convergence. We also derive a finite-particle entropy identity relative to the product target, giving exponential-in-time convergence of the empirical measure up to polynomial sampling errors. For propagation of chaos, we develop two complementary finite-time approaches. A synchronous coupling, combined with exponential moment estimates for the nonlinear mean-field diffusion, yields explicit single-exponential bounds in Wasserstein distance and kernel Stein discrepancy (KSD). Moving-product entropy gives joint-law relative entropy control relative to the evolving mean-field product law and, through entropy superadditivity and concentration, fixed-marginal relative entropy and total variation bounds and empirical KSD estimates. Under an additional $T_2$ inequality for the initial law, it also yields Wasserstein bounds. Combining these finite-time estimates with target convergence at a logarithmic cutoff time gives polynomial uniform-in-time propagation of chaos rates in expectation for empirical KSD and $W_2^2$, and for fixed-marginal total variation and $W_2^2$. All bounds control the last iterate in physical time. We also compare the two finite-time mechanisms and identify regimes in which each gives the sharper polynomial exponent.

Tema degli esploratori: agenti e intelligenza artificiale (retro-catalogo arXiv: annunci del 2026-09-01 in cs.LG).
Categorie arXiv: Machine Learning (stat.ML) ; Machine Learning (cs.LG); Probability (math.PR).
Pagina del lavoro: https://arxiv.org/abs/2608.28827 — 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 2026-10-17T08:13:26.884Z dalla pagina https://arxiv.org/catchup/cs.LG/2026-09-01?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).