{"ID":2840438,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.13085","arxiv_id":"2511.13085","title":"Non-asymptotic Analysis of Poisson randomized midpoint Langevin Monte Carlo","abstract":"The task of sampling from a high-dimensional distribution $π$ on $\\R^d$ is a fundamental algorithmic problem with applications throughout statistics, engineering, and the sciences. Consider the Langevin diffusion on $\\R^d$ \\begin{align*} \\dif X_t=-\\nabla U(X_t)dt+\\sqrt{2}dB_t, \\end{align*} under mild conditions, it admits $π(\\dif x)\\propto \\exp(-U(x))\\dif x$ as its unique stationary distribution. Recently, Kandasamy and Nagaraj (2024) introduced a stochastic algorithm called Poisson Randomized Midpoint Langevin Monte Carlo (PRLMC) to enhance the rate of convergence towards the target distribution $π$. In this paper, we first show that under mild conditions, the PRLMC, as a Markov chain, admits a unique stationary distribution $π_η$ ($η$ is the step size) and obtain the convergence rate of PRLMC to $π_η$ in total variation distance. Then we establish a sharp error bound between $π_η$ and $π$ under the 2-Wasserstein distance. Finally, we propose a decreasing-step size version of PRLMC and provide its convergence rate to $π$ which is nearly optimal.","short_abstract":"The task of sampling from a high-dimensional distribution $π$ on $\\R^d$ is a fundamental algorithmic problem with applications throughout statistics, engineering, and the sciences. Consider the Langevin diffusion on $\\R^d$ \\begin{align*} \\dif X_t=-\\nabla U(X_t)dt+\\sqrt{2}dB_t, \\end{align*} under mild conditions, it adm...","url_abs":"https://arxiv.org/abs/2511.13085","url_pdf":"https://arxiv.org/pdf/2511.13085v1","authors":"[\"Tian Shen\",\"Zhonggen Su\"]","published":"2025-11-17T07:33:40Z","proceeding":"math.ST","tasks":"[\"math.ST\",\"math.PR\"]","methods":"[\"Diffusion Model\"]","has_code":false}