We present a unified framework to analyze the global convergence of Langevin dynamics based algorithms for nonconvex finite-sum optimization with 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…
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48 results for “Gradient Langevin Dynamics”
On Random Subset Generalization Error Bounds and the Stochastic Gradient Langevin Dynamics Algorithmcs.IT
Unified bounds for random subset generalization error and improved SGD Langevin dynamics.
problem Generalization error bounds for random subsets and stochastic gradient Langevin dynamics.
method Unified framework based on Hellström and Durisi's work, extending bounds for Langevin dynamics.
result Unified and refined bounds for generalization error in stochastic gradient Langevin dynamics.
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.
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.
Improved sampling efficiency with Random Reshuffling for Langevin dynamics.
problem Sampling efficiency in stochastic gradient algorithms.
method Random Reshuffling for Stochastic Gradient Langevin Dynamics (SGLD).
result Random Reshuffling leads to improved performance in sampling.
The paper analyzes convergence of Langevin dynamics with time-dependent metrics.
problem Analyzing convergence of Langevin dynamics with time-dependent metrics.
method Formulated a modified gradient flow of the Kullback-Leibler divergence, selected a time-dependent relative Fisher information functional, and developed a time-dependent Hessian matrix condition.
result Proved convergence conditions for various Langevin dynamics.
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.
ICSGLD improves efficiency in posterior sampling for big data.
problem Efficient posterior sampling for large datasets.
method Embarrassingly parallel multiple-chain CSGLD with efficient interactions.
result ICSGLD is more efficient than a single-chain CSGLD.
NSGLD improves SGLD for non-convex optimization problems.
problem Optimizing non-convex objectives efficiently.
method Introducing non-reversible SGLD by adding an anti-symmetric matrix to the drift term of the Langevin diffusion.
result NSGLD converges faster to the same stationary distribution with non-asymptotic guarantees.
New algorithm improves convergence for non-convex problems with boundaries.
problem Optimizing non-convex problems with constraints.
method Reflected Gradient Langevin Dynamics with probabilistic representation.
result Promising convergence rates, faster than existing methods.
Enhances SGLD for log-concave posteriors with asynchronous computation.
problem Sampling log-concave posterior distributions efficiently.
method Integrates asynchronous computation into SGLD with delayed gradients.
result Convergence in measure is not significantly affected by delayed gradient information.
A new algorithm improves Bayesian federated learning by reducing communication overhead.
problem Bayesian federated learning constraints, including privacy, data ownership, and communication overhead.
method Proposes Quantised Langevin Stochastic Dynamics (QLSD) for Bayesian federated learning, using gradient compression and variance reduction techniques.
result Non-asymptotic and asymptotic convergence guarantees for QLSD and its improved versions.
Langevin Dynamics for Adaptive Inverse Reinforcement Learning of Stochastic Gradient Algorithmscs.LG
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)).
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.
FSGLD improves federated data sampling by correcting noisy gradients.
problem Noisy gradients and delayed communication in federated data.
method Conductive gradients to correct noisy gradients in distributed SGLD.
result FSGLD converges to true posterior even with delayed communication.
The paper analyzes variance reduction in stochastic gradient Langevin dynamics.
problem Reducing the variance of stochastic gradient estimators in Langevin dynamics.
method Central limit theorem and Poisson equation analysis for variance characterization.
result Anti-symmetric perturbations can reduce the variance of non-reversible Langevin dynamics.
Improved convergence rates for MFLD in various gradient estimators.
problem Proving convergence rates for mean-field Langevin dynamics with stochastic gradient updates.
method General framework for propagation of chaos, including finite-particle approximation, time-discretization, and stochastic gradient approximation.
result Improved convergence rates for SGD and SVRG settings.
New method improves sample diversity and efficiency from complex distributions.
problem Sampling from intractable un-normalized distributions with high auto-correlation.
method Stein self-repulsive dynamics using a repulsive force to push samples away from past trajectories.
result Significantly decreases auto-correlation and increases effective sample size.
Gradient-based Monte Carlo sampling algorithms, like Langevin dynamics and Hamiltonian Monte Carlo, are important methods for Bayesian inference. In large-scale settings, full-gradients are not affordable and thus stochastic gradients evaluated on mini-batches are used as a replacement. In order to reduce the high vari…
New method corrects bias in stochastic gradient samplers.
problem Bias in stochastic gradient samplers.
method Gradient-Guided Monte Carlo with stochastic gradients.
result Corrected sampler yields nonzero acceptance probabilities.
New rates for GLD and SGLD in infinite-dimensional spaces without dimensionality issues.
problem Gradient Langevin dynamics and SGLD convergence rates in high-dimensional spaces.
method Analysis of GLD and SGLD in infinite-dimensional Hilbert spaces, using stochastic differential equations and Markov chains.
result Derivation of dimension-free convergence rates for GLD and SGLD.
Adaptive Stochastic Gradient Langevin Dynamics: Taming Convergence and Saddle Point Escape Timecs.LG
In this paper, we propose a new adaptive stochastic gradient Langevin dynamics (ASGLD) algorithmic framework and its two specialized versions, namely adaptive stochastic gradient (ASG) and adaptive gradient Langevin dynamics(AGLD), for non-convex optimization problems. All proposed algorithms can escape from saddle poi…
A new algorithm flattens multi-modal distributions for better deep learning.
problem Bayesian learning in big data with multi-modal distributions.
method Contour Stochastic Gradient Langevin Dynamics (CSGLD) algorithm.
result The CSGLD algorithm avoids local traps in deep neural networks.
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 bound for KL-divergence between SGLD and Langevin diffusion.
Adaptive Langevin dynamics reduces bias in Bayesian inference with mini-batching.
problem Bias in posterior sampling due to mini-batching in Bayesian inference.
method Adaptive Langevin dynamics with dynamical friction to correct noise.
result Quantified bias in posterior distribution due to mini-batching.
Improved privacy analysis for stochastic gradient descent.
problem Analyzing privacy leakage in noisy stochastic gradient descent.
method Modeling Rényi divergence dynamics with Langevin diffusions, proving exponential privacy loss convergence for smooth and strongly convex objectives.
result Privacy loss converges exponentially fast for smooth and strongly convex objectives under constant step size.
Hybrid method improves sampling from multimodal distributions.
problem Sampling from multimodal posterior distributions efficiently.
method Jump-Diffusion Langevin Dynamics hybrid with Metropolis.
result Calibrated hybrid method outperforms pure methods.
Improved convergence for non-log-concave sampling.
problem Sampling from non-log-concave distributions.
method Novel conductance analysis of SGLD with auxiliary Markov Chain.
result SGLD achieves ε-sampling error with fewer evaluations.
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.
Extends Langevin dynamics for constrained domains.
problem Optimization of constrained probability measures.
method Mirror mean-field Langevin dynamics (MMFLD).
result Linear convergence guarantees and propagation of chaos results.
Proposes a new Langevin flow approach for VAEs.
problem Difficulty in constructing low variance ELBO for VAEs with large datasets.
method Integrates Langevin dynamic with quasi-symplectic integrator to improve posterior estimation.
result Shows theoretical and practical effectiveness compared to gradient flow-based methods.
In this paper, we propose a novel technique to implement stochastic gradient methods, which are beneficial for learning from large datasets, through accelerated stochastic dynamics. A stochastic gradient method is based on mini-batch learning for reducing the computational cost when the amount of data is large. The sto…
First order discretizations of Langevin diffusion can achieve better generalization error with additional smoothness assumptions.
problem Analyzing generalization error for first order discretizations of Langevin diffusion.
method Providing a sufficient smoothness condition to show that first order methods can achieve arbitrarily runtime complexity for a given expected generalization error.
result First order methods can achieve arbitrarily runtime complexity with additional smoothness assumptions.
Enhanced SMC uses gradients from CRN-PF in Langevin proposals for improved state and parameter estimation.
problem Challenges in high-dimensional parameter spaces for SMC.
method Leveraging gradients from a CRN-PF within a Langevin proposal.
result Higher effective sample size and more accurate parameter estimates.
We study sampling as optimization in the space of measures. We focus on gradient flow-based optimization with the Langevin dynamics as a case study. We investigate the source of the bias of the unadjusted Langevin algorithm (ULA) in discrete time, and consider how to remove or reduce the bias. We point out the difficul…
SGBD algorithm improves robustness in Bayesian sampling.
problem Inefficiency of existing MCMC algorithms in large datasets.
method Extends Barker MCMC to stochastic gradient framework, introducing bias-corrected version.
result SGBD is more robust to hyperparameter tuning and gradient noise.
Paper uses SGLD to recover signals from generative models, proving convergence under mild conditions.
problem Signal recovery from generative priors in compressed sensing.
method Stochastic Gradient Langevin Dynamics (SGLD) for signal recovery.
result SGLD converges to the true signal under mild assumptions on the generative model.
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.
Unbiased method for Bayesian posterior means using kinetic Langevin dynamics.
problem Estimating Bayesian posterior means efficiently and accurately.
method Combines advanced splitting methods with enhanced gradient approximations in a multilevel Monte Carlo approach.
result The method achieves unbiased estimates with finite variance and central limit theorem properties.
Geometry-informed irreversible perturbations for accelerated convergence of Langevin dynamicsstat.ME
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.
Proposes r2SGLD for efficient constrained exploration in non-convex learning.
problem Stagnation in high-temperature chains of reSGLD in distribution tails.
method r2SGLD: replica exchange with reflection steps in a bounded domain.
result Reflection steps enhance mixing rates with quadratic improvement in domain diameter.
fSGLD optimizes deep learning by favoring flat regions in the loss landscape.
problem Understanding and improving the behavior and generalization of deep learning algorithms.
method Flatness-Aware Stochastic Gradient Langevin Dynamics (fSGLD) that biases learning towards flat basins.
result fSGLD targets a flatness-biased Gibbs distribution with explicit excess risk guarantees.
Algorithm generates private continuous-time data for sensitive domains.
problem Private generation of continuous-time data for sensitive domains.
method Mean-field Langevin dynamics and noisy particle gradient descent.
result Strong privacy guarantees for one-time data contributions.
Paper improves generalization bounds for noisy stochastic algorithms.
problem Improving generalization bounds for noisy stochastic algorithms.
method Introduces Exponential Family Langevin Dynamics (EFLD) and establishes data-dependent expected stability based generalization bounds.
result Sharp generalization bounds with O(1/n) sample dependence and gradient discrepancy.
Finite-Sample Bounds for Adaptive Inverse Reinforcement Learning using Passive Langevin Dynamicscs.LG
Paper analyzes PSGLD for adaptive IRL with finite-sample bounds.
problem Estimating cost function of a forward learner using noisy gradients.
method Passive stochastic gradient Langevin dynamics (PSGLD) algorithm.
result Explicit bounds on 2-Wasserstein distance between PSGLD sample measure and stationary measure.
New algorithm speeds up sampling from complex distributions.
problem Efficiently sampling from non-log-concave distributions.
method Stochastic Proximal Samplers (SPS) based on SGLD and MALA.
result SPS-SGLD and SPS-MALA achieve faster sampling with reduced gradient complexity.
Paper explores low-precision SGLD for neural networks, reducing costs without sacrificing performance.
problem Infeasibility of low-precision sampling in large-scale scenarios.
method Developed low-precision SGLD with quantization function and full-precision gradient accumulators.
result Low-precision SGLD achieves comparable performance to full-precision SGLD with only 8 bits.
The paper analyzes the mean field Langevin dynamics and its convergence rate.
problem The convergence property of the mean field Langevin dynamics in the context of neural networks.
method The analysis uses a proximal Gibbs distribution and techniques from convex optimization.
result A concise convergence rate analysis of the mean field Langevin dynamics in both continuous and discrete time settings.