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We provide a nonasymptotic analysis of the convergence of the stochastic gradient Hamiltonian Monte Carlo (SGHMC) to a target measure in Wasserstein-2 distance without assuming log-concavity.
Laplace’s method revisited: weak convergence of probability measures
Chii-Ruey Hwang · 1980
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Recursive stochastic algorithms for global optimization in ℝ d \mathbb{R}^{d}
Saul B Gelfand and Sanjoy K Mitter · 1991
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Exponential convergence of Langevin distributions and their discrete approximations
Gareth O Roberts, Richard L Tweedie, et al · 1996
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Ergodicity for sdes and approximations: locally lipschitz vector fields and degenerate noise
Jonathan C Mattingly, Andrew M Stuart, and Desmond J Higham · 2002
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Langevin diffusions and metropolis-hastings algorithms
Gareth O Roberts and Osnat Stramer · 2002
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Bayesian learning via stochastic gradient Langevin dynamics
Max Welling and Yee W Teh · 2011
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Bayesian posterior sampling via stochastic gradient Fisher scoring
Sungjin Ahn, Anoop Korattikara, and Max Welling · 2012
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Stochastic Gradient Hamiltonian Monte Carlo
Tianqi Chen, Emily Fox, and Carlos Guestrin · 2014
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A complete recipe for stochastic gradient mcmc
Yi-An Ma, Tianqi Chen, and Emily Fox · 2015
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Theoretical guarantees for approximate sampling from smooth and log-concave densities
Arnak S Dalalyan · 2017
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Using perturbed underdamped Langevin dynamics to efficiently sample from probability distributions
AB Duncan, N Nüsken, and GA Pavliotis · 2017
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Nonasymptotic convergence analysis for the unadjusted Langevin algorithm
Alain Durmus, Eric Moulines, et al · 2017
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Non-convex learning via Stochastic Gradient Langevin Dynamics: a nonasymptotic analysis
Maxim Raginsky, Alexander Rakhlin, and Matus Telgarsky · 2017
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The promises and pitfalls of stochastic gradient Langevin dynamics
Nicolas Brosse, Alain Durmus, and Eric Moulines · 2018
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On sampling from a log-concave density using kinetic Langevin diffusions
Arnak S Dalalyan and Lionel Riou-Durand · 2018
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Global non-convex optimization with discretized diffusions
Murat A Erdogdu, Lester Mackey, and Ohad Shamir · 2018
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Non-asymptotic bounds for sampling algorithms without log-concavity
Mateusz B Majka, Aleksandar Mijatović, and Lukasz Szpruch · 2018
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Global convergence of Langevin dynamics based algorithms for nonconvex optimization
Pan Xu, Jinghui Chen, Difan Zou, and Quanquan Gu · 2018
Cited alongside, same era.
Rapid convergence of the unadjusted Langevin algorithm: Isoperimetry suffices
Santosh Vempala and Andre Wibisono · 2019
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Stochastic gradient Hamiltonian Monte Carlo methods with recursive variance reduction
Difan Zou, Pan Xu, and Quanquan Gu · 2019
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On stochastic gradient Langevin dynamics with dependent data streams in the logconcave case
Mathias Barkhagen, Ngoc Huy Chau, Éric Moulines, Miklós Rásonyi, Sotirios Sabanis, and Ying Zhang · 2021
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On stochastic gradient Langevin dynamics with dependent data streams: The fully nonconvex case
Ngoc Huy Chau, Éric Moulines, Miklos Rásonyi, Sotirios Sabanis, and Ying Zhang · 2021
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On the convergence of Langevin Monte Carlo: The interplay between tail growth and smoothness
Murat A Erdogdu and Rasa Hosseinzadeh · 2021
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The tamed unadjusted Langevin algorithm
Nicolas Brosse, Alain Durmus, Éric Moulines, and Sotirios Sabanis · 2019
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On fixed gain recursive estimators with discontinuity in the parameters
Huy N Chau, Chaman Kumar, Miklós Rásonyi, and Sotirios Sabanis · 2019
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User-friendly guarantees for the Langevin Monte Carlo with inaccurate gradient
Arnak S Dalalyan and Avetik Karagulyan · 2019
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High-dimensional Bayesian inference via the unadjusted Langevin algorithm
Alain Durmus, Eric Moulines, et al · 2019
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Couplings and quantitative contraction rates for Langevin dynamics
Andreas Eberle, Arnaud Guillin, and Raphael Zimmer · 2019
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Stochastic runge-kutta accelerates Langevin Monte Carlo and beyond
Xuechen Li, Yi Wu, Lester Mackey, and Murat A Erdogdu · 2019
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Is There an Analog of Nesterov Acceleration for MCMC?
Yi-An Ma, Niladri Chatterji, Xiang Cheng, Nicolas Flammarion, Peter Bartlett, and Michael I Jordan · 2019
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Towards a theory of non-log-concave sampling: first-order stationarity guarantees for Langevin Monte Carlo
Krishna Balasubramanian, Sinho Chewi, Murat A Erdogdu, Adil Salim, and Shunshi Zhang · 2022
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Stochastic gradient hamiltonian Monte Carlo for non-convex learning
Huy N Chau and Miklós Rásonyi · 2022
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Analysis of Langevin Monte Carlo from poincare to log-sobolev
Sinho Chewi, Murat A Erdogdu, Mufan Li, Ruoqi Shen, and Shunshi Zhang · 2022
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Convergence of Langevin Monte Carlo in chi-squared and rényi divergence
Murat A Erdogdu, Rasa Hosseinzadeh, and Shunshi Zhang · 2022
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Global convergence of stochastic gradient hamiltonian Monte Carlo for nonconvex stochastic optimization: nonasymptotic performance bounds and momentum-based acceleration
Xuefeng Gao, Mert Gürbüzbalaban, and Lingjiong Zhu · 2022
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Improved bounds for discretization of Langevin diffusions: Near-optimal rates without convexity
Wenlong Mou, Nicolas Flammarion, Martin J Wainwright, and Peter L Bartlett · 2022
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Towards a complete analysis of Langevin Monte Carlo: Beyond poincar \ \backslash ’e inequality
Alireza Mousavi-Hosseini, Tyler Farghly, Ye He, Krishnakumar Balasubramanian, and Murat A Erdogdu · 2023
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