{"ID":2840442,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.13093","arxiv_id":"2511.13093","title":"Convergence rate of randomized midpoint Langevin Monte Carlo","abstract":"The randomized midpoint Langevin Monte Carlo (RLMC), introduced by Shen and Lee (2019), is a variant of classical Unadjusted Langevin Algorithm. It was shown in the literature that the RLMC is an efficient algorithm for approximating high-dimensional probability distribution $π$. In this paper, we establish the exponential ergodicity of RLMC with constant step-size. Moreover, we design a dereasing-step size RLMC and provide its convergence rate in terms of a functional class distance.","short_abstract":"The randomized midpoint Langevin Monte Carlo (RLMC), introduced by Shen and Lee (2019), is a variant of classical Unadjusted Langevin Algorithm. It was shown in the literature that the RLMC is an efficient algorithm for approximating high-dimensional probability distribution $π$. In this paper, we establish the exponen...","url_abs":"https://arxiv.org/abs/2511.13093","url_pdf":"https://arxiv.org/pdf/2511.13093v1","authors":"[\"Ruinan Li\",\"Tian Shen\",\"Zhonggen Su\"]","published":"2025-11-17T07:48:04Z","proceeding":"math.ST","tasks":"[\"math.ST\",\"math.PR\"]","methods":"[]","has_code":false}