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The technique of modifying the geometry of a problem from Euclidean to Hessian metric has proved to be quite effective in optimization, and has been the subject of study for sampling.
Convex Analysis
R. Tyrrell Rockafellar · 1970
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On extensions of the Brunn-Minkowski and Prékopa-Leindler theorems, including inequalities for log concave functions, and with an application to the diffusion equation
Herm Jan Brascamp and Elliott H Lieb · 1976
Earlier work this paper cites.
The variational formulation of the Fokker–Planck equation
Richard Jordan, David Kinderlehrer, and Felix Otto · 1998
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Random walks on polytopes and an affine interior point method for linear programming
Ravindran Kannan and Hariharan Narayanan · 2012
Earlier work this paper cites.
Stochastic numerics for mathematical physics
Grigori Noah Milstein and Michael V Tretyakov · 2013
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Further and stronger analogy between sampling and optimization: Langevin Monte Carlo and gradient descent
Arnak Dalalyan · 2017
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Nonasymptotic convergence analysis for the unadjusted Langevin algorithm
Alain Durmus and Eric Moulines · 2017
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Mirrored Langevin Dynamics
Ya-Ping Hsieh, Ali Kavis, Paul Rolland, and Volkan Cevher · 2018
Cited alongside, same era.
Sampling as optimization in the space of measures: The Langevin dynamics as a composite optimization problem
Andre Wibisono · 2018
Cited alongside, same era.
User-friendly guarantees for the Langevin Monte Carlo with inaccurate gradient
Arnak S Dalalyan and Avetik Karagulyan · 2019
Cited alongside, same era.
High-dimensional bayesian inference via the unadjusted Langevin algorithm
Alain Durmus and Eric Moulines · 2019
Cited alongside, same era.
Quelques applications du transport optimal en analyse et en probabilités
Max Fathi · 2019
Cited alongside, same era.
Stochastic Runge-Kutta accelerates Langevin Monte Carlo and beyond
Xuechen Li, Yi Wu, Lester Mackey, and Murat A Erdogdu · 2019
Rapid convergence of the Unadjusted Langevin Algorithm: Isoperimetry suffices
Santosh Vempala and Andre Wibisono · 2019
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Efficient constrained sampling via the mirror-Langevin algorithm
Kwangjun Ahn and Sinho Chewi · 2020
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Exponential ergodicity of mirror-Langevin diffusions
Sinho Chewi, Thibaut Le Gouic, Chen Lu, Tyler Maunu, Philippe Rigollet, and Austin Stromme · 2020
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Strong self-concordance and sampling
Aditi Laddha, Yin Tat Lee, and Santosh Vempala · 2020
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Wasserstein control of Mirror Langevin Monte Carlo
Kelvin Shuangjian Zhang, Gabriel Peyré, Jalal Fadili, and Marcelo Pereyra · 2020
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Cited alongside, same era.
Ruilin Li, Hongyuan Zha, and Molei Tao · 2021
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