2021/12/23 by Sinho Chewi, Murat A. Erdogdu, Chewi, Sinho +7 · 1 citation
Mathematics · Medicine · #Advanced Neuroimaging Techniques and Applications #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (stat.ML) #Markov Chains and Monte Carlo Methods #Medical Imaging Techniques and Applications #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.2112.12662
openalex publication_date 2021/12/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Classically, the continuous-time Langevin diffusion converges exponentially fast to its stationary distribution π under the sole assumption that π satisfies a Poincaré inequality. Using this fact to provide guarantees for the discrete-time Langevin Monte Carlo (LMC) algorithm, however, is considerably more challenging due to the need for working with chi-squared or Rényi divergences, and prior works have largely focused on strongly log-concave targets. In this work, we provide the first convergence guarantees for LMC assuming that π satisfies either a Latała--Oleszkiewicz or modified log-Sobolev inequality, which interpolates between the Poincaré and log-Sobolev settings. Unlike prior works, our results allow for weak smoothness and do not require convexity or dissipativity conditions.