Improved Guarantees for Langevin Monte Carlo with Average Smoothness
We establish improved nonasymptotic bounds for Langevin Monte Carlo in the strongly log-concave setting, when the error is measured by the Wasserstein distance. The main result shows that the discretization error is governed by an average coordinate-wise smoothness constant, rather than by the usual global smoothness constant. The proof is short and probabilistic, and relies on a refined use of the synchronous coupling. We further show that the same ideas lead to improved bounds for variable step sizes, for potentials whose Laplacian is Lipschitz-continuous, and for finite-sum problems sampled by stochastic-gradient Langevin dynamics with fixed point control variates. In the Laplacian-smo...
| Authors | Arnak S. Dalalyan, Avetik Karagulyan |
|---|---|
| Primary category | math.ST |
| Published | 29 May 2026 |
| Last updated at source | 29 May 2026 |
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