SGD's stationary distribution is Boltzmann-Gibbs with temperature equal to step-size, concentrating exponentially on minimum-energy critical points.
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Derives KL and TV error bounds for kTULA and tRLMC schemes, giving near-optimal ilde O(ε^{-1/2}) complexity for kTULA and ilde O(ε^{-1}) for tRLMC under log-Sobolev sampling.
A pilot-fitted log-scale proxy of the growth score plus quantile thresholds yields a deterministic local denominator that nearly matches the exact G⋆-envelope and beats random-denominator tamed SGLD at similar production cost.
New RSLMC sampling algorithms achieve uniform-in-time W2 error bounds of order O(sqrt(d) h) under gradient Lipschitz and log-Sobolev assumptions, with modified versions for superlinear gradient growth and supporting numerical examples.
citing papers explorer
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What is the long-run distribution of stochastic gradient descent? A large deviations analysis
SGD's stationary distribution is Boltzmann-Gibbs with temperature equal to step-size, concentrating exponentially on minimum-energy critical points.
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Error estimates for tamed Euler and Randomized Euler schemes for SDEs with locally Lipschitz drift with applications to non-logconcave sampling and optimization
Derives KL and TV error bounds for kTULA and tRLMC schemes, giving near-optimal ilde O(ε^{-1/2}) complexity for kTULA and ilde O(ε^{-1}) for tRLMC under log-Sobolev sampling.
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Deterministic Denominator Design for Localized Tamed Stochastic Gradient Langevin Dynamics
A pilot-fitted log-scale proxy of the growth score plus quantile thresholds yields a deterministic local denominator that nearly matches the exact G⋆-envelope and beats random-denominator tamed SGLD at similar production cost.
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When Langevin Monte Carlo Meets Randomization: New Sampling Algorithms with Non-asymptotic Error Bounds beyond Log-Concavity and Gradient Lipschitzness
New RSLMC sampling algorithms achieve uniform-in-time W2 error bounds of order O(sqrt(d) h) under gradient Lipschitz and log-Sobolev assumptions, with modified versions for superlinear gradient growth and supporting numerical examples.