mlsanityData to 7 Oct 2026

A connection between Tempering and Entropic Mirror Descent

arXiv 2310.11914 ↗First posted 18 Oct 2023stat.CO math.OC math.STcited by 16

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Abstract (arXiv)

This paper explores the connections between tempering (for Sequential Monte Carlo; SMC) and entropic mirror descent to sample from a target probability distribution whose unnormalized density is known. We establish that tempering SMC corresponds to entropic mirror descent applied to the reverse Kullback-Leibler (KL) divergence and obtain convergence rates for the tempering iterates. Our result motivates the tempering iterates from an optimization point of view, showing that tempering can be seen as a descent scheme of the KL divergence with respect to the Fisher-Rao geometry, in contrast to Langevin dynamics that perform descent of the KL with respect to the Wasserstein-2 geometry. We exploit the connection between tempering and mirror descent iterates to justify common practices in SMC and derive adaptive tempering rules that improve over other alternative benchmarks in the literature.

Key facts. Cited by 16 papers in the map (data through 7 Oct 2026). Builds on 19 of its 47 references that are in the map. First posted on arXiv 18 Oct 2023.

Builds on

19 of 47 references.

References · 19

  1. 2016Linear Convergence of Gradient and Proximal-Gradient Methods Under the Polyak-Lojasiewicz Conditioncited by 526
  2. 2019Rapid Convergence of the Unadjusted Langevin Algorithm: Isoperimetry Sufficescited by 224
  3. 2017Stein Variational Gradient Descent as Gradient Flowcited by 149
  4. 2018Analysis of Langevin Monte Carlo via convex optimizationcited by 126
  5. 2018Sampling as optimization in the space of measures: The Langevin dynamics as a composite optimization problemcited by 123
  6. 2016Relatively-Smooth Convex Optimization by First-Order Methods, and Applicationscited by 108
  7. 2019High-Order Langevin Diffusion Yields an Accelerated MCMC Algorithmcited by 36
  8. 2020An invitation to sequential Monte Carlo samplerscited by 33
  9. 2022Mirror Descent with Relative Smoothness in Measure Spaces, with application to Sinkhorn and EMcited by 33
  10. 2022Birth-death dynamics for sampling: Global convergence, approximations and their asymptoticscited by 30
  11. 2015Provable Bayesian Inference via Particle Mirror Descentcited by 23
  12. 2021Convergence Rates of Gradient Methods for Convex Optimization in the Space of Measurescited by 19
7 more
  1. 2023An Explicit Expansion of the Kullback-Leibler Divergence along its Fisher-Rao Gradient Flowcited by 16
  2. 2021Adaptive Importance Sampling meets Mirror Descent: a Bias-variance tradeoffcited by 13
  3. 2020All in the Exponential Family: Bregman Duality in Thermodynamic Variational Inferencecited by 11
  4. 2023Adaptive Annealed Importance Sampling with Constant Rate Progresscited by 7
  5. 2020Annealed Importance Sampling with q-Pathscited by 6
  6. 2015Variational Optimization of Annealing Schedulescited by 5
  7. 2020Mirror Descent Algorithms for Minimizing Interacting Free Energycited by 3

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Cited by year (2026 to 7 Oct)

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

16 papers.

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  1. 2024Sampling in Unit Time with Kernel Fisher-Rao Flowcited by 27
  2. 2024Fisher-Rao Gradient Flow: Geodesic Convexity and Functional Inequalitiescited by 13
  3. 2024Theoretical Guarantees for Variational Inference with Fixed-Variance Mixture of Gaussianscited by 11
  4. 2024Stein transport for Bayesian inferencecited by 11
  5. 2024Provable Convergence and Limitations of Geometric Tempering for Langevin Dynamicscited by 10
  6. 2024Efficient, Multimodal, and Derivative-Free Bayesian Inference With Fisher-Rao Gradient Flowscited by 9
  7. 2025Learning Boltzmann Generators via Constrained Mass Transportcited by 8
  8. 2025Sequential Monte Carlo approximations of Wasserstein--Fisher--Rao gradient flowscited by 5
  9. 2024Inclusive KL Gradient Flows: Otto-Wasserstein, Fisher-Rao-Gaussian, and Local-Estimator Dynamicscited by 4
  10. 2024Connections between sequential Bayesian inference and evolutionary dynamicscited by 4
  11. 2025A note on the unique properties of the Kullback--Leibler divergence for sampling via gradient flowscited by 4
  12. 2025An operator splitting analysis of Wasserstein--Fisher--Rao gradient flowscited by 2
4 more
  1. 2023Sinkhorn Flow: A Continuous-Time Framework for Understanding and Generalizing the Sinkhorn Algorithmcited by 1
  2. 2025Asymptotically exact variational flows via involutive MCMC kernelscited by 1
  3. 2026Properties and limitations of geometric tempering for gradient flow dynamicscited by 0
  4. 2026Preservation of Log-Concavity and Convergence of Wasserstein-Fisher-Rao Gradient Flowscited by 0