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Langevin diffusion is a powerful method for nonconvex optimization, which enables the escape from local minima by injecting noise into the gradient.
Functional analysis and semi-groups
Phillips, R. S · 1957
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Asymptotic evaluation of certain Markov process expectations for large time
Donsker, M. D · 1975
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Laplace’s method revisited: Weak convergence of probability measures
Hwang, C.-R · 1980
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Thermodynamical approach to the traveling salesman problem: An efficient simulation algorithm
Černỳ, V · 1985
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Global optimization via the Langevin equation
Gidas, B · 1985
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Diffusions for global optimization
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Diffusion for global optimization in ℝ n \mathbb{R}^{n}
Chiang, T.-S · 1987
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Simulated tempering: a new Monte Carlo scheme
Marinari, E · 1992
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Acceleration of stochastic approximation by averaging
Polyak, B. T · 1992
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Annealing Markov chain Monte Carlo with applications to ancestral inference
Geyer, C. J · 1995
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Some Gronwall-type inequalities and applications
Dragomir, S. S · 2003
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On swapping and simulated tempering algorithms
Zheng, Z · 2003
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Parallel tempering: Theory, applications, and new perspectives
Earl, D. J · 2005
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A simple proof of the Poincaré inequality for a large class of probability measures
Bakry, D · 2008
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Exchange frequency in replica exchange molecular dynamics
Sindhikara, D · 2008
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Sparse regression learning by aggregation and Langevin Monte Carlo
Dalalyan, A · 2009
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Conditions for rapid mixing of parallel and simulated tempering on multimodal distributions
Woodard, D. B · 2009
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Asymptotic behavior of dissipative systems
Hale, J. K · 2010
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Escaping the local minima via simulated annealing: Optimization of approximately convex functions
Belloni, A · 2015
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Sampling from a log-concave distribution with projected Langevin Monte Carlo
Bubeck, S · 2015
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Escaping from saddle points—online stochastic gradient for tensor decomposition
Ge, R · 2015
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On graduated optimization for stochastic non-convex problems
Hazan, E · 2016
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On large-batch training for deep learning: Generalization gap and sharp minima
Keskar, N. S · 2016
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Hybrid switching diffusions: Properties and applications
Yin, G · 2010
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On the infinite swapping limit for parallel tempering
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Analysis and geometry of Markov diffusion operators
Bakry, D · 2013
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Convergence of probability measures
Billingsley, P · 2013
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Introductory lectures on convex optimization: A basic course
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Continuous martingales and Brownian motion
Revuz, D · 2013
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Dalalyan, A. S · 2017
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Nonasymptotic convergence analysis for the unadjusted Langevin algorithm
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Non-convex learning via stochastic gradient Langevin dynamics: A nonasymptotic analysis
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