Langevin algorithms improve training of very deep neural networks, especially for image classification.
problem Training very deep neural networks is challenging due to increased non-linearity and the risk of getting stuck in local minima.
method Comparison of Langevin and non-Langevin algorithms for training deep neural networks, introduction of Layer Langevin algorithm.
result Langevin algorithms, especially Layer Langevin, lead to significant improvements in training deep neural networks, particularly for image classification tasks.
New algorithms improve sampling from complex distributions.
problem Sampling from complex probability distributions efficiently.
method Regime-switching Langevin dynamics and Monte Carlo algorithms.
result Convergence guarantees and iteration complexities provided.
Study non-asymptotic Langevin Monte Carlo for Gibbs distributions.
problem Sampling from Gibbs distributions with dissipative potentials.
method Langevin-type algorithms based on Liptser--Shiryaev theory and Poincaré inequalities.
result Upper bound on 2-Wasserstein distance for accurate approximation.
New Langevin Monte Carlo algorithms for sampling from nonsmooth distributions.
problem Sampling from distributions with nonsmooth convex composite potentials.
method Leveraging Bregman--Moreau envelopes and proximal operators in mirror descent.
result Efficiency in sampling from nonsmooth distributions, extending existing methods.
Paper analyzes and accelerates Langevin Monte Carlo methods using large deviations theory.
problem High-dimensional sampling problems in machine learning.
method Unified approach using large deviations theory to study and accelerate Langevin dynamics variants.
result Efficiency of Langevin dynamics variants demonstrated through numerical experiments.
Adaptive algorithm improves convergence rate of Langevin dynamics.
problem Improving convergence rate of Langevin dynamics.
method Adaptive non-reversible stochastic gradient Langevin dynamics algorithm.
result Improved convergence rate of the algorithm.
New Langevin algorithms improve sampling efficiency in high dimensions.
problem Sampling from log-concave and smooth distributions in high dimensions.
method Combining splitting and accurate integration methods for P P P -th order Langevin dynamics. result LMC algorithms converge faster with better dimension dependence as P P P increases. Gradient-descent-based algorithms and their stochastic versions have widespread applications in machine learning and statistical inference. In this work we perform an analytic study of the performances of one of them, the Langevin algorithm, in the context of noisy high-dimensional inference. We employ the Langevin alg…
Unified approach for sampling non-differentiable and heavy-tailed targets.
problem Sampling non-differentiable and heavy-tailed distributions using Langevin algorithms.
method Anchored Langevin dynamics, which modifies the Langevin diffusion with a smooth reference potential and multiplicative scaling.
result Non-asymptotic guarantees in the 2-Wasserstein distance to the target distribution.
New algorithm improves sampling from constrained spaces.
problem Sampling from constrained spaces efficiently.
method Metropolis-adjusted Mirror Langevin algorithm.
result Unbiased sampling with improved mixing time.
The Langevin Algorithm's stationary distribution is shown to be sub-exponential or sub-Gaussian under certain conditions.
problem Understanding the properties of the Langevin Algorithm's stationary distribution.
method Analysis using a rotation-invariant moment generating function (Bessel function) to study the stationary dynamics of the Langevin Algorithm.
result Concentration results for the Langevin Algorithm's stationary distribution π η π_η π η are established, showing it is sub-exponential or sub-Gaussian under convex or strongly convex potential conditions. Paper analyzes and compares ELF algorithms for federated learning.
problem Improving efficiency and privacy in federated learning.
method Proposes P-ELF, D-ELF, and B-ELF algorithms with primal, dual, and bidirectional compression.
result Provides non-asymptotic convergence guarantees under Log-Sobolev inequality.
Optimal preconditioning improves Langevin sampling efficiency.
problem Improving sampling efficiency in high-dimensional target distributions.
method Optimal preconditioning using Fisher information, applied to MALA.
result Adaptive MCMC scheme significantly outperforms other methods.
Improved Langevin algorithms with prior diffusion achieve dimension-independent convergence for non-log-concave distributions.
problem Understanding the dimension dependency of computational complexity in high-dimensional sampling.
method Investigation of prior diffusion technique for log-Sobolev inequality target distributions.
result Modified Langevin algorithm achieves dimension-independent KL divergence convergence.
Paper proposes Langevin dynamics for adaptive IRL of stochastic gradient algorithms.
problem Estimating reward functions from noisy gradient estimates of stochastic gradient agents.
method Generalized Langevin dynamics algorithm for IRL.
result Proposed algorithms asymptotically generate samples proportional to exp(R(θ)).
Noise-corrected Langevin algorithm improves sampling from noisy data.
problem Sampling from noisy data with biased score function.
method Noise-corrected Langevin algorithm using noisy score function.
result Bias due to noisy data is removed, improving sampling accuracy.
Langevin algorithms enhance training of deep neural networks for stochastic control problems.
problem Training acceleration for deep neural networks in stochastic control problems.
method Application of Langevin algorithms to minimize the loss of deep neural networks in stochastic control problems.
result Langevin algorithms improve training on various stochastic control problems.
This paper resolves the Langevin Algorithm's mixing time for log-concave distributions.
problem Resolving the mixing time of the Langevin Algorithm for log-concave sampling.
method Introducing Privacy Amplification by Iteration to analyze Rényi divergence and Optimal Transport smoothing.
result Optimal mixing bounds for the Langevin Algorithm in log-concave sampling settings.
A new algorithm solves semidefinite programs using Langevin diffusion.
problem Optimizing semidefinite programs with diagonal constraints.
method Langevin diffusion on a product manifold of spheres.
result Langevin algorithm achieves ε accuracy in Ω(ε^-5) iterations.
New Langevin method achieves third order convergence for strongly log-concave distributions.
problem Sampling from complex distributions efficiently.
method Underdamped Langevin diffusion with third order convergence.
result Achieves 2-Wasserstein error of ε in O(√d/ε^1/3) steps under additional Lipschitz condition.
Paper proposes new Langevin samplers for sampling from log-concave distributions with superlinear gradient growth.
problem Sampling from log-concave distributions with superlinear gradient growth.
method Proposes two novel discretizations of kinetic Langevin SDEs, showing contractivity and log-Sobolev inequality.
result Establishes non-asymptotic bounds in 2-Wasserstein distance between sampled distributions and target measures.
New algorithms improve Langevin Monte Carlo efficiency.
problem High computational cost of classical Langevin Monte Carlo.
method Integrates ensemble feature into LMC, constraining gradient approximations.
result Constrained Ensemble Langevin Monte Carlo reduces gradient computation.
Novel geometry-informed irreversible perturbation accelerates Langevin dynamics convergence.
problem Accelerating convergence of Langevin dynamics for Bayesian computation.
method Geometry-informed irreversible perturbation of Riemannian manifold Langevin dynamics.
result Improves estimation performance over irreversible perturbations that ignore geometry.
Study Langevin Monte Carlo for sampling non-log-concave distributions.
problem Sampling from non-log-concave distributions, especially Gaussian mixtures.
method Discretizations of overdamped Langevin diffusions.
result Numerical simulations compare Langevin Monte Carlo algorithms' performance.
New algorithm extends LMC to more complex potentials.
problem Addressing limitations of existing LMC methods.
method Inexact Proximal Langevin Algorithm (IPLA).
result Improved convergence rates and broader applicability.
New methods use transport maps to improve Langevin dynamics for sampling.
problem Sampling high-dimensional, non-Gaussian distributions efficiently.
method Apply transport maps to accelerate Langevin dynamics convergence.
result Discretized processes converge to target distribution with non-asymptotic bounds.
Study on Langevin dynamics convergence rates and their application to GAN training.
problem Understanding the long-term behavior of Langevin dynamics equations.
method Analytical and numerical methods to study convergence rates of underdamped mean-field Langevin dynamics.
result Exponential convergence rate results for the Langevin dynamics under various conditions.
We present a unified framework to analyze the global convergence of Langevin dynamics based algorithms for nonconvex finite-sum optimization with n n n component functions. At the core of our analysis is a direct analysis of the ergodicity of the numerical approximations to Langevin dynamics, which leads to faster conver…
Paper approximates risk measures using SGD with Langevin dynamics.
problem Approximating arbitrary law invariant risk measures.
method Stochastic Gradient Langevin Dynamics (SGD-Langevin) for general risk measures.
result Non-asymptotic convergence rates of the approximation algorithm.
Algorithms that tackle deep exploration -- an important challenge in reinforcement learning -- have relied on epistemic uncertainty representation through ensembles or other hypermodels, exploration bonuses, or visitation count distributions. An open question is whether deep exploration can be achieved by an incrementa…
New method controls bias in unadjusted Hamiltonian Monte Carlo and underdamped Langevin.
problem Bias in unadjusted Hamiltonian Monte Carlo and underdamped Langevin samplers.
method Delocalization of bias technique applied to these samplers.
result Control W 2 W_2 W 2 bias with O ( K ) O(\sqrt{K}) O ( K ) integration steps for high-dimensional distributions. Mirror Langevin Algorithm converges with zero bias.
problem Achieving convergence with zero bias in discrete-time sampling.
method Discretization of Mirror Langevin Diffusion and mean-square analysis.
result Mirror Langevin Algorithm converges with zero bias.
We formulate gradient-based Markov chain Monte Carlo (MCMC) sampling as optimization on the space of probability measures, with Kullback-Leibler (KL) divergence as the objective functional. We show that an underdamped form of the Langevin algorithm performs accelerated gradient descent in this metric. To characterize t…
Proves convergence of PSGLA for sampling non-convex potentials.
problem Sampling from non-convex potentials with stability.
method Combines ULA and proximal optimization with stability analysis.
result First proof of convergence for PSGLA on non-convex potentials.
Improved error estimate for SGLD sampling algorithm.
problem Establishing a precise error bound for SGLD.
method Sharp uniform-in-time error estimate for SGLD under mild assumptions.
result Uniform-in-time O ( η 2 ) O(η^2) O ( η 2 ) bound for KL-divergence between SGLD and Langevin diffusion. The Riemannian Langevin Algorithm samples from manifolds efficiently.
problem Sampling from distributions on manifolds with log-Sobolev inequality.
method Riemannian Langevin Algorithm, log-Sobolev inequality, self-concordance extension, stochastic smoothness bounding.
result The Riemannian Langevin Algorithm converges rapidly to the target density.
Study on convergence of Langevin dynamics for zero-sum games in probability distributions.
problem Analyzing convergence of Langevin dynamics for zero-sum games in probability distributions.
method Proved exponential and biased convergence guarantees for mean-field and finite-particle min-max Langevin dynamics.
result Explicit iteration complexity for finite-particle algorithms to approximate equilibrium distributions.
Paper improves convergence rate of Langevin Dynamics algorithms.
problem Sampling problems and non-convex optimization in machine learning.
method Stochastic Variance Reduced Gradient Langevin Dynamics and Stochastic Recursive Gradient Langevin Dynamics with improved convergence rates.
result Proves convergence to objective distribution under weaker conditions.
In this paper, we provide new insights on the Unadjusted Langevin Algorithm. We show that this method can be formulated as a first order optimization algorithm of an objective functional defined on the Wasserstein space of order 2 2 2 . Using this interpretation and techniques borrowed from convex optimization, we give a …
New method optimizes non-linear functionals over probability measures.
problem Optimizing non-linear functionals defined over probability measures.
method N-particle underdamped Langevin algorithm with spacetime discretization.
result Converges globally in total variation distance.
Replica exchange Langevin diffusion accelerates nonconvex optimization.
problem Nonconvex optimization challenges in machine learning.
method Replica exchange Langevin diffusion, discretization analysis.
result Replica exchange accelerates convergence to global minima.
MAFLA improves sampling from heavy-tailed distributions using MH-inspired corrections.
problem Sampling from heavy-tailed and multimodal distributions when neither target nor proposal densities can be evaluated.
method Metropolis-Adjusted Fractional Langevin Algorithm (MAFLA) with Score Balance Matching.
result MAFLA significantly improves finite-time sampling accuracy over unadjusted fractional Langevin dynamics.
The paper analyzes convergence rates of Langevin dynamics and Proximal Sampler using Φ Φ Φ -divergence.
problem Analyzing convergence rates of Langevin dynamics and Proximal Sampler.
method Extending mixing time analyses to Φ Φ Φ -divergence, using strong data processing inequalities. result Convergence of Φ Φ Φ -divergence to 0 exponentially fast along Unadjusted Langevin Algorithm and Proximal Sampler. Paper analyzes Gibbs and Langevin Monte Carlo for interpolation regime, showing generalization from low errors.
problem Analyzing Gibbs and Langevin Monte Carlo in overparameterized interpolation regime.
method Data-dependent bounds and stability under approximation with Langevin Monte Carlo.
result Generalization is signaled by small training errors in noisy regime, with bounds stable under approximation.
New Langevin algorithm works well even for rough distributions.
problem Sampling from non-smooth distributions.
method Simple Langevin algorithm without smoothness assumptions.
result Algorithm performs well even with discontinuous gradients.
New algorithm for solving minimax problems over distributions converges to Nash equilibrium.
problem Solving minimax problems over probability distributions.
method Symmetric Mean-field Langevin Dynamics (MFL-AG and MFL-ABR) with weighted averaging and best response dynamics.
result Converges to mixed Nash equilibrium with average-iterate and last-iterate convergence.
New algorithms improve inference in non-differentiable models.
problem Inference and learning in latent variable models with non-differentiable densities.
method Proximal interacting particle Langevin algorithms (PIPLA).
result Nonasymptotic bounds and effectiveness demonstrated in various models.
Traditionally, neural networks are parameterized using optimization procedures such as stochastic gradient descent, RMSProp and ADAM. These procedures tend to drive the parameters of the network toward a local minimum. In this article, we employ alternative "sampling" algorithms (referred to here as "thermodynamic para…