mlsanityData to 7 Oct 2026

Faster Differentially Private Samplers via R'enyi Divergence Analysis of Discretized Langevin MCMC

arXiv 2010.14658 ↗First posted 27 Oct 2020cs.LG cs.CR cs.DScited by 27

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Abstract (arXiv)

Various differentially private algorithms instantiate the exponential mechanism, and require sampling from the distribution exp(-f) for a suitable function f. When the domain of the distribution is high-dimensional, this sampling can be computationally challenging. Using heuristic sampling schemes such as Gibbs sampling does not necessarily lead to provable privacy. When f is convex, techniques from log-concave sampling lead to polynomial-time algorithms, albeit with large polynomials. Langevin dynamics-based algorithms offer much faster alternatives under some distance measures such as statistical distance. In this work, we establish rapid convergence for these algorithms under distance measures more suitable for differential privacy. For smooth, strongly-convex f, we give the first results proving convergence in R'enyi divergence. This gives us fast differentially private algorithms for such f. Our techniques and simple and generic and apply also to underdamped Langevin dynamics.

Key facts. Cited by 27 papers in the map (data through 7 Oct 2026). First posted on arXiv 27 Oct 2020.

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Citing papers per year: 2021: 3; 2022: 8; 2023: 8; 2024: 5; 2025: 2; 2026: 1.

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  1. 2021Differential Privacy Dynamics of Langevin Diffusion and Noisy Gradient Descentcited by 71
  2. 2022Privacy of Noisy Stochastic Gradient Descent: More Iterations without More Privacy Losscited by 60
  3. 2024Langevin Unlearning: A New Perspective of Noisy Gradient Descent for Machine Unlearningcited by 48
  4. 2022Private Convex Optimization via Exponential Mechanismcited by 47
  5. 2023Faster high-accuracy log-concave sampling via algorithmic warm startscited by 44
  6. 2023Towards a Complete Analysis of Langevin Monte Carlo: Beyond Poincar'e Inequalitycited by 31
  7. 2023Improved dimension dependence of a proximal algorithm for samplingcited by 29
  8. 2022One Parameter Defense -- Defending against Data Inference Attacks via Differential Privacycited by 26
  9. 2023Improved Discretization Analysis for Underdamped Langevin Monte Carlocited by 26
  10. 2022Resolving the Mixing Time of the Langevin Algorithm to its Stationary Distribution for Log-Concave Samplingcited by 21
  11. 2024Certified Machine Unlearning via Noisy Stochastic Gradient Descentcited by 13
  12. 2023Initialization Matters: Privacy-Utility Analysis of Overparameterized Neural Networkscited by 9
15 more
  1. 2021Sampling from Log-Concave Distributions with Infinity-Distance Guaranteescited by 8
  2. 2024The Poisson Midpoint Method for Langevin Dynamics: Provably Efficient Discretization for Diffusion Modelscited by 6
  3. 2022Convergence of the Inexact Langevin Algorithm in KL Divergence with Application to Score-based Generative Modelscited by 4
  4. 2022Differentially Private Sampling from Rashomon Sets, and the Universality of Langevin Diffusion for Convex Optimizationcited by 3
  5. 2024Privacy of SGD under Gaussian or Heavy-Tailed Noise: Guarantees without Gradient Clippingcited by 3
  6. 2024R'enyi-infinity constrained sampling with d3 membership queriescited by 3
  7. 2021Can Stochastic Gradient Langevin Dynamics Provide Differential Privacy for Deep Learning?cited by 2
  8. 2023Privacy Risk for anisotropic Langevin dynamics using relative entropy boundscited by 2
  9. 2022Sampling from Log-Concave Distributions over Polytopes via a Soft-Threshold Dikin Walkcited by 1
  10. 2022Recycling Scraps: Improving Private Learning by Leveraging Intermediate Checkpointscited by 1
  11. 2023Differentially Private Topological Data Analysiscited by 1
  12. 2023Differentially Private Statistical Inference through β-Divergence One Posterior Samplingcited by 0
  13. 2025Poisson Midpoint Method for Log Concave Sampling: Beyond the Strong Error Lower Boundscited by 0
  14. 2025R'enyi Differential Privacy for Heavy-Tailed SDEs via Fractional Poincar'e Inequalitiescited by 0
  15. 2026On the Stability of Spherical Hellinger-Kantorovich Flows and Their Implications for Differential Privacycited by 0