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R'enyi Tracking Bounds for Langevin Dynamics with Moving Targets

arXiv 2609.17577 ↗First posted 25 Aug 2026stat.ML cs.LGcited by 0

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Abstract (arXiv)

We study Langevin diffusion and Langevin Monte Carlo (LMC) when the target distribution changes over time. Under a log-Sobolev inequality (LSI), we derive non-asymptotic R'enyi-divergence guarantees for tracking the current target. The framework covers continuous-time Langevin diffusion and its discretizations. We then apply the results to nonsmooth sampling based on successive Moreau envelopes. For this scheme, we give explicit choices of the smoothing parameters and step sizes, together with corresponding complexity bounds. To our knowledge, these are the first non-asymptotic R'enyi-divergence tracking bounds for Langevin dynamics with discrete target updates.

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References · 11

  1. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,101
  2. 2014Theoretical guarantees for approximate sampling from smooth and log-concave densitiescited by 208
  3. 2015Non-asymptotic convergence analysis for the Unadjusted Langevin Algorithmcited by 197
  4. 2016Efficient Bayesian computation by proximal Markov chain Monte Carlo: when Langevin meets Moreaucited by 84
  5. 2013Proximal Markov chain Monte Carlo algorithmscited by 46
  6. 2024Provable Benefit of Annealed Langevin Monte Carlo for Non-log-concave Samplingcited by 23
  7. 2025Non-asymptotic Analysis of Diffusion Annealed Langevin Monte Carlo for Generative Modellingcited by 11
  8. 2024Provable Convergence and Limitations of Geometric Tempering for Langevin Dynamicscited by 10
  9. 2024Shifted Composition III: Local Error Framework for KL Divergencecited by 7
  10. 2025Diffusion at Absolute Zero: Langevin Sampling Using Successive Moreau Envelopes [conference paper]cited by 6
  11. 2026Forward-KL Convergence of Time-Inhomogeneous Langevin Diffusionscited by 2

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