No Markovian coupling captures the TV decay rate for kinetic Langevin with quadratic potential; a non-Markovian optimal-control coupling interprets and strengthens existing sharp bounds while removing assumptions for OBABO.
Chatterji, Yasin Abbasi-Yadkori, Peter L
10 Pith papers cite this work. Polarity classification is still indexing.
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Combining random reshuffling and Richardson-Romberg extrapolation yields cubic bias refinement and better MSE for constant-step SGD on structured non-monotone variational inequalities.
Conditions for long-time L^p Wasserstein contraction are derived for non-globally dissipative diffusions, extending to non-elliptic processes with a one-dimensional characterization via the maximal eigenvalue of a Feynman-Kac operator.
Proposes KIPLMC algorithms based on joint parameter-latent diffusions with nonasymptotic Wasserstein-2 rates under strong concavity, claiming improved dimension dependence over prior Langevin methods.
Optimal rates for non-log-concave sampling and log-partition estimation are sometimes equal to or faster than optimization rates, but polynomial-time algorithms fall short of near-optimal performance.
SGD on multiclass cross-entropy loss alternates between curvature-driven oscillations and stable regimes but self-stabilizes to enable best-iterate convergence with large learning rates for linear and two-layer models.
A stochastic Runge-Kutta Schrödinger-Föllmer sampler (SRKSFS) is introduced with a proven O(h^{3/2} |ln h|) convergence rate in L2-Wasserstein distance, extended to data-driven sampling from empirical measures.
A Hessian-free stochastic Runge-Kutta LMC algorithm achieves strong order 1.5 with two gradient evaluations per step and uniform-in-time convergence O(d^{3/2} h^{3/2}) in non-log-concave settings.
A unified large deviations analysis is proposed to study acceleration mechanisms in variants of overdamped Langevin Monte Carlo methods, supported by numerical experiments.
citing papers explorer
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On couplings for kinetic Langevin diffusions
No Markovian coupling captures the TV decay rate for kinetic Langevin with quadratic potential; a non-Markovian optimal-control coupling interprets and strengthens existing sharp bounds while removing assumptions for OBABO.
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Shuffling the Data, Stretching the Step-size: Sharper Bias in constant step-size SGD
Combining random reshuffling and Richardson-Romberg extrapolation yields cubic bias refinement and better MSE for constant-step SGD on structured non-monotone variational inequalities.
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Long-time $L^p$ Wasserstein contraction for diffusion processes without global dissipativity
Conditions for long-time L^p Wasserstein contraction are derived for non-globally dissipative diffusions, extending to non-elliptic processes with a one-dimensional characterization via the maximal eigenvalue of a Feynman-Kac operator.
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Kinetic Interacting Particle Langevin Monte Carlo
Proposes KIPLMC algorithms based on joint parameter-latent diffusions with nonasymptotic Wasserstein-2 rates under strong concavity, claiming improved dimension dependence over prior Langevin methods.
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Convergence Rates for Non-Log-Concave Sampling and Log-Partition Estimation
Optimal rates for non-log-concave sampling and log-partition estimation are sometimes equal to or faster than optimization rates, but polynomial-time algorithms fall short of near-optimal performance.
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SGD at the Edge of Stability: Stochastic Stabilization with Large Learning Rates
SGD on multiclass cross-entropy loss alternates between curvature-driven oscillations and stable regimes but self-stabilizes to enable best-iterate convergence with large learning rates for linear and two-layer models.
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Accelerated Schr\"odinger-F\"ollmer samplers
A stochastic Runge-Kutta Schrödinger-Föllmer sampler (SRKSFS) is introduced with a proven O(h^{3/2} |ln h|) convergence rate in L2-Wasserstein distance, extended to data-driven sampling from empirical measures.
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Accelerating Langevin Monte Carlo via Efficient Stochastic Runge--Kutta Methods beyond Log-Concavity
A Hessian-free stochastic Runge-Kutta LMC algorithm achieves strong order 1.5 with two gradient evaluations per step and uniform-in-time convergence O(d^{3/2} h^{3/2}) in non-log-concave settings.
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Accelerating Langevin Monte Carlo Sampling: A Large Deviations Analysis
A unified large deviations analysis is proposed to study acceleration mechanisms in variants of overdamped Langevin Monte Carlo methods, supported by numerical experiments.
- On the global convergence of gradient flow for wide shallow models beyond homogeneous nonlinearities