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Analysis of a zeroth-order multiscale sampler: strong convergence, convergence of ergodic averages and weak convergence

  • Antonin Della Noce
  • Urbain Vaes
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Abstract

In many practical applications of Bayesian inference, it is difficult or undesirable to compute the gradient of the negative log-posterior, motivating the study of derivative-free samplers, also called zeroth-order samplers. The aim of this paper is to generalize and rigorously analyze a multiscale derivative-free sampler recently proposed in the literature by Pavliotis, Stuart and Vaes (2022). In the discrete-time setting, the multiscale sampler we study bears a strong resemblance to other recently proposed methods, such as the so-called zeroth-order perturbed stochastic gradient descent algorithm (Jin et al., 2018) and the zeroth-order Langevin Monte Carlo algorithm by Roy et al. (2022). We present error estimates with respect to all the parameters of the problem, both in the continuous-time and discrete-time settings. The error estimates are in three different metrics: strong convergence, convergence of ergodic averages, and uniform-in-time weak convergence.

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Cite

BibTeXRIS
BibTeX
@misc{noce2026analysis,
  title = {{Analysis of a zeroth-order multiscale sampler: strong convergence, convergence of ergodic averages and weak convergence}},
  author = {Antonin Della Noce and Urbain Vaes},
  howpublished = {HAL},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.17037},
  eprint = {2610.17037},
  archivePrefix = {arXiv},
  url = {https://hal.science/hal-05843830v1},
}
RIS
TY  - UNPB
TI  - Analysis of a zeroth-order multiscale sampler: strong convergence, convergence of ergodic averages and weak convergence
AU  - Antonin Della Noce
AU  - Urbain Vaes
PY  - 2026
DA  - 2026/10/12
PB  - HAL
DO  - 10.48550/arxiv.2610.17037
UR  - https://hal.science/hal-05843830v1
AB  - In many practical applications of Bayesian inference, it is difficult or undesirable to compute the gradient of the negative log-posterior, motivating the study of derivative-free samplers, also called zeroth-order samplers. The aim of this paper is to generalize and rigorously analyze a multiscale derivative-free sampler recently proposed in the literature by Pavliotis, Stuart and Vaes (2022). In the discrete-time setting, the multiscale sampler we study bears a strong resemblance to other recently proposed methods, such as the so-called zeroth-order perturbed stochastic gradient descent algorithm (Jin et al., 2018) and the zeroth-order Langevin Monte Carlo algorithm by Roy et al. (2022). We present error estimates with respect to all the parameters of the problem, both in the continuous-time and discrete-time settings. The error estimates are in three different metrics: strong convergence, convergence of ergodic averages, and uniform-in-time weak convergence.
ER  -