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The stochastic gradient Langevin Dynamics is one of the most fundamental algorithms to solve sampling problems and non-convex optimization appearing in several machine learning applications.
Laplace’s method revisited: weak convergence of probability measures
C.-R. Hwang · 1980
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Logarithmic Sobolev inequalities and stochastic Ising models
R. Holley and D. W. Stroock · 1986
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Diffusion for global optimization in ℝ n \mathbb{R}^{n}
T.-S. Chiang, C.-R. Hwang, and S. J. Sheu · 1987
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Recursive stochastic algorithms for global optimization in ℝ d \mathbb{R}^{d}
S. B. Gelfand and S. K. Mitter · 1991
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The variational formulation of the Fokker–Planck equation
R. Jordan, D. Kinderlehrer, and F. Otto · 1998
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A strong approximation theorem for stochastic recursive algorithms
V. S. Borkar and S. K. Mitter · 1999
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Generalization of an inequality by Talagrand and links with the logarithmic Sobolev inequality
F. Otto and C. Villani · 2000
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Ergodicity for SDEs and approximations: locally Lipschitz vector fields and degenerate noise
J. C. Mattingly, A. M. Stuart, and D. J. Higham · 2002
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A simple proof of the Poincaré inequality for a large class of probability measures
D. Bakry, F. Barthe, P. Cattiaux, and A. Guillin · 2008
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Estimation of information theoretic measures for continuous random variables
F. Pérez-Cruz · 2008
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A note on Talagrand’s transportation inequality and logarithmic Sobolev inequality
P. Cattiaux, A. Guillin, and L.-M. Wu · 2010
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Bayesian learning via stochastic gradient Langevin dynamics
M. Welling and Y. W. Teh · 2011
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Accelerating stochastic gradient descent using predictive variance reduction
R. Johnson and T. Zhang · 2013
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Poincaré and logarithmic Sobolev inequalities by decomposition of the energy landscape
G. Menz and A. Schlichting · 2014
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Metastability: a Potential-Theoretic Approach , volume 351
A. Bovier and F. Den Hollander · 2016
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Variance reduction in stochastic gradient Langevin dynamics
K. A. Dubey, S. J Reddi, S. A. Williamson, B. Poczos, A. J. Smola, and E. P. Xing · 2016
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Non-convex learning via stochastic gradient langevin dynamics: a nonasymptotic analysis
M. Raginsky, A. Rakhlin, and M. Telgarsky · 2017
SSRGD: Simple stochastic recursive gradient descent for escaping saddle points
Z. Li · 2019
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Rapid convergence of the unadjusted Langevin algorithm: Isoperimetry suffices
S. Vempala and A. Wibisono · 2019
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High-Dimensional Statistics: A Non-Asymptotic Viewpoint , volume 48
M. J. Wainwright · 2019
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SpiderBoost and momentum: Faster variance reduction algorithms
Z. Wang, K. Ji, Y. Zhou, Y. Liang, and V. Tarokh · 2019
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Riemannian langevin algorithm for solving semidefinite programs
M. B. Li and M. A. Erdogdu · 2020
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ProxSARAH: An efficient algorithmic framework for stochastic composite nonconvex optimization
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On the theory of variance reduction for stochastic gradient Monte Carlo
N. Chatterji, N. Flammarion, Y. Ma, P. Bartlett, and M. Jordan · 2018
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Sampling as optimization in the space of measures: The Langevin dynamics as a composite optimization problem
A. Wibisono · 2018
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Global convergence of Langevin dynamics based algorithms for nonconvex optimization
P. Xu, J. Chen, D. Zou, and Q. Gu · 2018
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Subsampled stochastic variance-reduced gradient Langevin dynamics
D. Zou, P. Xu, and Q. Gu · 2018
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Further and stronger analogy between sampling and optimization: Langevin Monte Carlo and gradient descent
A. Dalalyan
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Theoretical guarantees for approximate sampling from smooth and log-concave densities
A. S. Dalalyan
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N. H. Pham, L. M. Nguyen, D. T. Phan, and Q. Tran-Dinh · 2020
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P. Chen, J. Lu, and L. Xu · 2021
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Stochastic gradient Langevin dynamics with variance reduction
Z. Huang and S. Becker · 2021
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Faster convergence of stochastic gradient Langevin Dynamics for non-log-concave sampling
D. Zou, P. Xu, and Q. Gu · 2021
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K. Balasubramanian, S. Chewi, M. A. Erdogdu, A. Salim, and M. Zhang · 2022
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