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PreprintCC BY 4.0arXiv

Entropy hypocoercivity and query complexity for the bouncy particle sampler

  • Jianfeng Lu
  • Yinchen Luo
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Abstract

We study convergence in relative entropy of the bouncy particle sampler with Gaussian velocity refreshment, for a target e−U on ℝd with U m-strongly convex and L-smooth, and condition number κ=L/m. For initial laws with bounded density relative to equilibrium, we show that the relative entropy decays exponentially up to an arbitrary additive error δ, with a rate that depends only logarithmically on the density bound and on δ. From a Gaussian cold start and with a suitably chosen refreshment rate, the relative entropy falls below δ after time Õ(√(d/m)). Combined with exact simulation by windowed thinning, this gives an expected gradient-query complexity of Õ(d√κ), improving the Õ(d2√κ) bound based on L2 hypocoercivity.

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Cite

BibTeXRIS
BibTeX
@misc{lu2026entropy,
  title = {{Entropy hypocoercivity and query complexity for the bouncy particle sampler}},
  author = {Jianfeng Lu and Yinchen Luo},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.25354},
  eprint = {2610.25354},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.25354},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Entropy hypocoercivity and query complexity for the bouncy particle sampler
AU  - Jianfeng Lu
AU  - Yinchen Luo
PY  - 2026
DA  - 2026/10/18
PB  - arXiv
DO  - 10.48550/arxiv.2610.25354
UR  - https://arxiv.org/abs/2610.25354
AB  - We study convergence in relative entropy of the bouncy particle sampler with Gaussian velocity refreshment, for a target e^−U on ℝ^d with U m-strongly convex and L-smooth, and condition number κ=L/m. For initial laws with bounded density relative to equilibrium, we show that the relative entropy decays exponentially up to an arbitrary additive error δ, with a rate that depends only logarithmically on the density bound and on δ. From a Gaussian cold start and with a suitably chosen refreshment rate, the relative entropy falls below δ after time Õ(√(d/m)). Combined with exact simulation by windowed thinning, this gives an expected gradient-query complexity of Õ(d√κ), improving the Õ(d^2√κ) bound based on L^2 hypocoercivity.
ER  -