The Performance Of The Unadjusted Langevin Algorithm Without Smoothness Assumptions

• URL: http://arxiv.org/abs/2502.03458v1
• Date: Wed, 05 Feb 2025 18:55:54 GMT
• Title: The Performance Of The Unadjusted Langevin Algorithm Without Smoothness Assumptions
• Authors: Tim Johnston, Iosif Lytras, Nikolaos Makras, Sotirios Sabanis,
• Abstract summary: We propose a Langevin-based algorithm that does not rely on popular but computationally challenging techniques. We derive non-asymptotic guarantees for the convergence of the algorithm to the target distribution. Non-asymptotic distances are also provided for the performance of the algorithm as an bounds.
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• Abstract: In this article, we study the problem of sampling from distributions whose densities are not necessarily smooth nor log-concave. We propose a simple Langevin-based algorithm that does not rely on popular but computationally challenging techniques, such as the Moreau Yosida envelope or Gaussian smoothing. We derive non-asymptotic guarantees for the convergence of the algorithm to the target distribution in Wasserstein distances. Non asymptotic bounds are also provided for the performance of the algorithm as an optimizer, specifically for the solution of associated excess risk optimization problems.

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