{"ID":2856450,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.11571","arxiv_id":"2510.11571","title":"Robust Online Sampling from Possibly Moving Target Distributions","abstract":"We suppose we are given a list of points $x_1, \\dots, x_n \\in \\mathbb{R}$, a target probability measure $μ$ and are asked to add additional points $x_{n+1}, \\dots, x_{n+m}$ so that $x_1, \\dots, x_{n+m}$ is as close as possible to the distribution of $μ$; additionally, we want this to be true uniformly for all $m$. We propose a simple method that achieves this goal. It selects new points in regions where the existing set is lacking points and avoids regions that are already overly crowded. If we replace $μ$ by another measure $μ_2$ in the middle of the computation, the method dynamically adjusts and allows us to keep the original sampling points. $x_{n+1}$ can be computed in $\\mathcal{O}(n)$ steps and we obtain state-of-the-art results. It appears to be an interesting dynamical system in its own right; we analyze a continuous mean-field version that reflects much of the same behavior.","short_abstract":"We suppose we are given a list of points $x_1, \\dots, x_n \\in \\mathbb{R}$, a target probability measure $μ$ and are asked to add additional points $x_{n+1}, \\dots, x_{n+m}$ so that $x_1, \\dots, x_{n+m}$ is as close as possible to the distribution of $μ$; additionally, we want this to be true uniformly for all $m$. We p...","url_abs":"https://arxiv.org/abs/2510.11571","url_pdf":"https://arxiv.org/pdf/2510.11571v1","authors":"[\"François Clément\",\"Stefan Steinerberger\"]","published":"2025-10-13T16:17:41Z","proceeding":"math.OC","tasks":"[\"math.OC\",\"cs.DS\",\"math.ST\"]","methods":"[]","has_code":false}