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.
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.
Langevin MCMC samples efficiently from Riemannian manifolds with geometric Euler-Murayama analysis.
problem Efficient sampling from Gibbs distributions on Riemannian manifolds.
method Geometric Langevin MCMC, discretization error bound, contraction guarantee for Langevin Diffusion.
result Langevin MCMC iterates converge to the target distribution after a number of steps proportional to the inverse square of the desired accuracy.
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…
ULA estimates covariance of log-concave distributions efficiently.
problem Estimating covariance matrices of log-concave distributions efficiently.
method Unadjusted Langevin algorithm (ULA) for sampling and covariance estimation.
result Sample complexity of single-chain ULA is smaller than that of parallel ULA by a logarithmic factor.
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.
New method uses higher-order Langevin dynamics for efficient parallel sampling.
problem Efficient parallel sampling from high-dimensional log-concave distributions.
method Combines higher-order Langevin dynamics with blockwise Lagrange polynomial interpolation.
result Reduces the number of parallel points required for a target accuracy.
Study of Langevin dynamics for tensor PCA recovery in high dimensions.
problem Recovering hidden signal vectors (spikes) from noisy Gaussian tensor observations.
method Langevin dynamics approach for nonconvex optimization.
result Sample complexity matches the single-spike case but degrades for all spikes.
New sampling method for heavy-tailed distributions using Langevin Algorithm.
problem Sampling from heavy-tailed distributions efficiently.
method Transformed Unadjusted Langevin Algorithm on specific transformations.
result Polynomial-order oracle complexities for certain heavy-tailed densities.
Study uses neural nets to learn multi-index models in high dimensions, reducing complexity.
problem Learning multi-index models in high-dimensional data.
method Mean-field Langevin dynamics with neural networks.
result Effective dimension controls sample and computational complexity, potentially reducing it.
Study improves sampling from complex distributions using annealed Langevin Monte Carlo.
problem Sampling from non-log-concave and multimodal distributions.
method Annealed Langevin Monte Carlo algorithm with theoretical guarantees.
result Oracle complexity of O(dβ²A²/ε⁶) for achieving ε² accuracy in Kullback-Leibler divergence.
A new method for sampling from complex distributions using Langevin samplers.
problem Sampling from unnormalized Boltzmann densities.
method Probability flow ODE derived from linear stochastic interpolants, employing Langevin samplers.
result Efficient simulation of the flow with non-asymptotic convergence rate.
We study the problem of sampling from a distribution p ∗ ( x ) ∝ exp ( − U ( x ) ) p^*(x) \propto \exp\left(-U(x)\right) p ∗ ( x ) ∝ exp ( − U ( x ) ) , where the function U U U is L L L -smooth everywhere and m m m -strongly convex outside a ball of radius R R R , but potentially nonconvex inside this ball. We study both overdamped and underdamped Langevin MCMC and establish upper bound…
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.
Langevin Dynamics fails to sample from mixture distributions efficiently.
problem Analyzing Langevin Dynamics for sampling from mixture distributions.
method Theoretical analysis of Langevin Dynamics and proposing Chained-Langevin Dynamics.
result Langevin Dynamics fails to sample from mixture distributions efficiently.
Improved sampling for high-dimensional posteriors with underdamped Langevin.
problem Scalability issues in high-dimensional problems with approximate Thompson sampling.
method Underdamped Langevin Monte Carlo for accelerated posterior concentration.
result Logarithmic regret improvement from i l d e O ( d ) \mathcal{ ilde O}(d) i l d e O ( d ) to i l d e O ( d ) \mathcal{ ilde O}(\sqrt{d}) i l d e O ( d ) . 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. Framework infers Langevin dynamics from stochastic observations of latent systems.
problem Inferring non-stationary Langevin dynamics from indirect stochastic observations.
method Non-parametric framework explicitly modeling stochastic observation process and non-stationary latent dynamics.
result Correct inference of non-stationary dynamics requires accounting for non-equilibrium states and observation duration.
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…
Paper analyzes complexity of PSGLA for sampling log-concave distributions.
problem Sampling from log-concave distributions with composite potentials.
method Uses primal-dual interpretation and duality gap to analyze PSGLA complexity.
result Complexity of PSGLA is O ( 1 / ε 2 ) O(1/\varepsilon^2) O ( 1/ ε 2 ) for strongly convex potentials. 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 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.
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.
New simulation method tackles sign problem in quantum fields.
problem Sign problem in real-time dynamics of quantum fields.
method Inspired by reinforcement learning, complex Langevin approach with learned optimal kernels.
result Significant extension of real-time simulations in 1+1d scalar field theory.
A new sampling method reduces computational cost for high-dimensional log-concave distributions.
problem High computational cost of ULMC in high dimensions.
method Random Coordinate ULMC (RC-ULMC) selects a single coordinate per iteration.
result RC-ULMC is cheaper than classical ULMC, especially in highly skewed and high-dimensional problems.
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.
Improved Thompson sampling for bandits with Langevin algorithms.
problem Thompson sampling's computational inefficiency in generating posterior samples.
method Developed Langevin algorithms for approximate sampling with posterior concentration guarantees.
result Logarithmic regret with constant computational complexity.
Enhanced SMC 2 ^2 2 uses gradients from CRN-PF in Langevin proposals for improved state and parameter estimation.
problem Challenges in high-dimensional parameter spaces for SMC 2 ^2 2 . method Leveraging gradients from a CRN-PF within a Langevin proposal.
result Higher effective sample size and more accurate parameter estimates.
New methods improve efficiency of sampling algorithms for complex systems.
problem Efficiently sampling from complex, high-dimensional probability distributions.
method Randomized Runge-Kutta-Nyström methods tailored for Hamiltonian flows.
result Quantitative 5 / 2 5/2 5/2 -order L 2 L^2 L 2 -accuracy in approximating Hamiltonian flows. New method proves dimension-free convergence for ULD in KL divergence.
problem Polynomial scaling of existing convergence guarantees in high dimensions.
method Refined KL local error framework, focusing on tr(H) instead of d.
result First dimension-free KL divergence bounds for discretized ULD.
New sampling algorithms for complex distributions without log-concavity.
problem Efficient sampling from complex, high-dimensional distributions.
method Randomized splitting Langevin Monte Carlo (RSLMC) algorithm.
result Uniform-in-time error bounds for RSLMC and RLMC algorithms.
This paper improves sampling from complex distributions using Langevin dynamics.
problem Pathological behaviors in normalizing flows for complex distributions.
method A Metropolis adjusted Langevin algorithm (MALA) to sample in the latent space.
result The method preserves tractability of the likelihood and works with any pre-trained NF network.
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…
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 sampler tackles complex discrete energy landscapes efficiently.
problem Stagnation in gradient-based discrete samplers for non-convex settings.
method DREXEL sampler with Replica Exchange and Adjusted Metropolis.
result Proves samplers satisfy detailed balance and converge to target distribution.
Paper tackles noisy and expensive likelihoods in complex models.
problem Calibrating parameters in complex models with noisy and expensive evaluations.
method Ensemble Kalman methods and Langevin-based methods for inverse problems.
result Ensemble Kalman methods perform well in noisy conditions, while Langevin methods are adversely affected.
Improved PoC for MFLD reduces approximation error and provides model ensemble guarantees.
problem Quantifying optimization complexity in mean-field Langevin dynamics.
method Refined defective log-Sobolev inequality for neural network training.
result Improved PoC result with reduced approximation error and theoretical model ensemble guarantees.
LMC improves sampling from complex distributions using quasi-random sequences.
problem Sampling from complex high-dimensional distributions with high accuracy.
method Using completely uniformly distributed (CUD) sequences in Langevin Monte Carlo (LMC) to generate Gaussian perturbations.
result LMC with low-discrepancy CUD sequences achieves smaller estimation error than standard LMC.
SLMC improves sampling efficiency for high-dimensional distributions.
problem Sampling from high-dimensional distributions is computationally challenging.
method SLMC projects Langevin updates onto subsampled eigenblocks of a time-varying preconditioner.
result SLMC offers superior adaptability and computational efficiency compared to traditional methods.
A new sampler for complex discrete distributions efficiently updates all variables in parallel.
problem Sampling complex high-dimensional discrete distributions efficiently and accurately.
method Discrete Langevin proposal (DLP) for parallel coordinate updates with controlled stepsize.
result DLP efficiently explores high-dimensional and strongly correlated variables with asymptotic bias of zero for log-quadratic distributions.
BLADE uses Bayesian methods to discover complex systems from scarce data.
problem Efficiently discovering governing equations of complex dynamical systems from limited data.
method Combines replica-exchange stochastic gradient Langevin Monte Carlo with active learning.
result Reduces measurement requirements by 60% for Lotka-Volterra and 40% for Burgers' equation.
New algorithms improve sampling from constrained distributions.
problem Sampling from distributions constrained to convex bodies.
method Penalized Langevin Dynamics and Underdamped Monte Carlo methods.
result Improved convergence rates for constrained sampling problems.
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.
New algorithms improve sampling from constrained distributions.
problem Generating samples from distributions under constraints.
method Kinetic Langevin dynamics and splitting schemes.
result Improved complexity bounds over existing methods.
Proposes efficient sampling methods for solving linear inverse problems.
problem Solving linear inverse problems with computational efficiency and accuracy.
method Higher-order Langevin diffusion with pre-conditioning and annealing.
result Provable sampling from posterior distributions with accelerated convergence.
A new sampling method, RC-LMC, reduces computational cost for high-dimensional log-concave distributions.
problem High computational cost of LMC in high dimensions.
method RC-LMC updates only one coordinate at a time, adding noise.
result RC-LMC is more efficient than LMC in high dimensions, especially for skewed distributions.
Tractable model explains market dynamics using Langevin and SUSY QM.
problem Understanding non-linear market dynamics and option pricing.
method Langevin dynamics mapped to QM, using SUSY to find solutions.
result NES model provides accurate option pricing with a single volatility parameter.
LaPSRL achieves optimal regret for isoperimetric RL distributions.
problem Designing RL algorithms with sublinear regret for non-log-concave distributions.
method Posterior Sampling (PSRL) and Langevin sampling (LaPSRL) for isoperimetric distributions.
result LaPSRL achieves order-optimal regret and subquadratic complexity.