Convergence in total variation for the kinetic Langevin algorithm

2024/07/12 by Joseph Lehec, Lehec, Joseph
Computer Science · Mathematics · #35H10 #65C05 #68W20 #Analysis of PDEs (math.AP) #Computational Complexity (cs.CC) #FOS: Computer and information sciences #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Statistical Methods and Inference #Stochastic Gradient Optimization Techniques

paper · pdf · doi:10.48550/arxiv.2407.09301

openalex publication_date 2024/07/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove non asymptotic total variation estimates for the kinetic Langevin algorithm in high dimension when the target measure satisfies a Poincaré inequality and has gradient Lipschitz potential. The main point is that the estimate improves significantly upon the corresponding bound for the non kinetic version of the algorithm, due to Dalalyan. In particular the dimension dependence drops from O(n) to O(√ n).

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