arXiv Statistics ML
Provable Non-Acceleration of Standard Strang Splittings of Kinetic Langevin Dynamics
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Penalized Nonreversible Langevin for Constrained Sampling
The paper introduces penalized nonreversible Langevin algorithms for sampling from a target distribution constrained to a compact convex set. It combines a squared distance penalty with skew-symmetric perturbations that preserve the penalized Gibbs distribution, and provides nonasymptotic total variation and Wasserstein bounds under various smoothness and contraction assumptions. Numerical experiments demonstrate the methods on constrained Bayesian regression, classification, neural networks, and truncated sampling, highlighting acceleration in a stochastic quadratic model.
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Near-Linear Accuracy Bounds for Moreau--Yosida Unadjusted Langevin Sampling
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Reflected Proximal Dynamics for Accelerated High-Accuracy Log-Concave Sampling
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Improved Analysis for Hessian-free High-resolution Monte Carlo Sampling
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arXiv Statistics ML
Sep 25
Global Convergence of Third-Order Langevin Dynamics for Non-Convex Optimization via Simulated Annealing
The paper establishes global convergence guarantees for third‑order Langevin dynamics applied to non‑convex optimization via simulated annealing with fixed friction and decreasing noise. It shows that, under dissipativity, regularity, and low‑temperature functional‑inequality assumptions, a logarithmic cooling schedule drives objective values to the global minimum with a barrier‑controlled kinetic rate, and that polynomially decreasing step sizes preserve this rate for both exact‑force‑integral and midpoint three‑stage discretizations. Numerical experiments on a double‑well problem and high‑dimensional neural‑network objectives demonstrate that third‑order Langevin schemes outperform overdamped Langevin dynamics and, in some cases, the one‑gradient UBU integrator in terms of terminal‑success point estimates and post‑quench test accuracy.
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Fast PAC Global Optimization via Restarted Langevin: Exploration, Exploitation, and Degenerate Cooling
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