Double-Loop Unadjusted Langevin Algorithm
Authors: Paul Rolland, Armin Eftekhari, Ali Kavis, Volkan Cevher
ICML 2020 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | This work proposes a new annealing step-size schedule for ULA, which allows to prove new convergence guarantees for sampling from a smooth log-concave distribution, which are not covered by existing state-of-the-art convergence guarantees. To establish this result, we derive a new theoretical bound that relates the Wasserstein distance to total variation distance between any two log-concave distributions that complements the reach of Talagrand T2 inequality. |
| Researcher Affiliation | Academia | 1LIONS, Ecole Polytechnique Fédérale de Lausanne, Switzerland 2Department of Mathematics and Mathematical Statistics, Umea University, Sweden. |
| Pseudocode | Yes | Algorithm 1 Double-loop Unadjusted Langevin Algorithm (DL-ULA) and Algorithm 2 DL-MYULA are provided. |
| Open Source Code | No | The paper does not contain any statement about making code open source or providing a link to a code repository. |
| Open Datasets | No | The paper is theoretical and focuses on analyzing sampling algorithms for probability distributions, rather than conducting experiments on specific datasets. Therefore, there is no mention of training data. |
| Dataset Splits | No | The paper is theoretical and does not involve empirical validation on datasets, thus no validation splits are mentioned. |
| Hardware Specification | No | The paper does not provide any specific details about the hardware used for computational work or experiments. |
| Software Dependencies | No | The paper does not provide specific software dependencies with version numbers. |
| Experiment Setup | No | The paper defines parameters for its algorithms (e.g., 'nk = LM 2dk2e3k', 'γk = Lde 2k') as part of the theoretical analysis, but these are not 'experimental setup' details in the sense of hyperparameters for an empirical evaluation (e.g., learning rates, batch sizes, optimizers). |