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.
Error estimates found between SGD with momentum and Langevin diffusion.
problem Quantifying the difference between SGD with momentum and Langevin diffusion.
method Established error estimates using 1-Wasserstein and total variation distances.
result Quantitative error estimates between SGD with momentum and underdamped Langevin diffusion.
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.
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.
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.
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.
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.
We present a unified framework to analyze the global convergence of Langevin dynamics based algorithms for nonconvex finite-sum optimization with 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…
SAGD uses Langevin algorithm for efficient gradient descent.
problem Efficiently approximating gradients in complex models.
method Langevin algorithm for biased but asymptotically accurate gradients.
result Theoretical convergence guarantee for SAGD.
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 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.
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.
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.
SGLB boosts machine learning with Langevin diffusion for multimodal loss functions.
problem Dealing with multimodal loss functions in machine learning.
method Stochastic Gradient Langevin Boosting (SGLB) based on Langevin diffusion equation.
result SGLB guarantees global convergence for multimodal loss functions.
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.
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…
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)).
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.
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.
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 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.
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.
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.
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…
New analysis for sampling from non-convex distributions with dependent data.
problem Sampling from non-logconcave distributions in stochastic optimization.
method Stochastic Gradient Langevin Dynamics (SGLD) with dependent data streams.
result Sharper and uniform convergence estimates in L1-Wasserstein distance. 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.
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(η2) bound for KL-divergence between SGLD and Langevin diffusion. Discretizations of Langevin diffusions provide a powerful method for sampling and Bayesian inference. However, such discretizations require evaluation of the gradient of the potential function. In several real-world scenarios, obtaining gradient evaluations might either be computationally expensive, or simply impossibl…
SGLDiff approximates Bayesian posterior distributions with subsampling error.
problem Approximating Bayesian posterior distributions in large-scale data settings.
method Stochastic Gradient Langevin Diffusion (SGLDiff) with subsampling.
result The Wasserstein distance between the posterior and SGLDiff's limiting distribution is bounded by a fractional power of the mean waiting time.
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.
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.
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.
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.
Study of Langevin processes and their convergence rates for non-convex problems.
problem Convergence of Langevin processes and SGD for non-convex optimization problems.
method Quantitative analysis of convergence rates for discrete Langevin-like processes.
result The convergence of SGD for non-convex problems depends on the potential function and additive noise.
Adaptively preconditions SGLD for faster convergence and better generalization.
problem Pathological curvature in deep network loss landscapes.
method Adaptive estimation of noise parameters to precondition isotropic gradient noise.
result Adaptively preconditioned SGLD achieves faster convergence and generalization equivalent of SGD.
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 TUSLA improves learning of non-convex neural networks.
problem Optimizing non-convex loss functions in neural networks with superlinear gradient growth.
method Tamed Unadjusted Stochastic Langevin Algorithm (TUSLA) based on SGLD with taming technology.
result Finite-time guarantees for TUSLA to find approximate minimizers of empirical and population risks.
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.
Simplified SGD interpretation as Ito process for broader applicability.
problem Lack of generality in current SGD interpretation.
method Introduced a simplified scheme for discrete-time approximation of Ito process.
result Flexibly interprets SGD and SGLD, providing insights into their asymptotic properties.
Paper analyzes SGLD for nonconvex optimization with local conditions.
problem Analyzing sampling algorithms for nonconvex optimization.
method Non-asymptotic estimates for SGLD under local conditions.
result Establishes error bounds for expected excess risk.
New algorithm samples from log concave distributions efficiently.
problem Sampling from log concave distributions efficiently.
method Stochastic Proximal Langevin Algorithm (SPLA) with potential splitting.
result Established nonasymptotic convergence rates for SPLA.
New algorithms for sampling and optimization without tuning.
problem Efficient sampling and optimization over probability measures.
method Optimization on the space of probability measures, using gradient flows.
result Strong theoretical guarantees and similar performance to optimally tuned algorithms.
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.
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.
New methods improve neural network training by sampling from target distributions.
problem Optimization procedures like SGD drive parameters to local minima.
method Thermodynamic parameterization using discretized stochastic differential equations.
result Partitioned numerical algorithms converge faster and more robustly.
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.
We study the problem of sampling from a probability distribution π on $\rset^d$ which has a density \wrt\ the Lebesgue measure known up to a normalization factor $x \mapsto \rme^{-U(x)} / \int_{\rset^d} \rme^{-U(y)} \rmd y$. We analyze a sampling method based on the Euler discretization of the Langevin stochastic dif…
New algorithm tackles optimization problems with discontinuous gradients in finance and insurance.
problem Optimization problems with discontinuous stochastic gradients in finance and insurance.
method Langevin dynamics based algorithm e-THεO POULA. result Non-asymptotic error bounds and expected excess risk estimates for e-THεO POULA.