A Dynamical System View of Langevin-Based Non-Convex Sampling

Authors: Mohammad Reza Karimi Jaghargh, Ya-Ping Hsieh, Andreas Krause

NeurIPS 2023 | Conference PDF | Archive PDF | Plain Text | LLM Run Details

Reproducibility Variable Result LLM Response
Research Type Theoretical To address these issues, we develop a novel framework that lifts the above issues by harnessing several tools from the theory of dynamical systems. Our key result is that, for a large class of state-of-the-art sampling schemes, their last-iterate convergence in Wasserstein distances can be reduced to the study of their continuous-time counterparts, which is much better understood. Coupled with standard assumptions of MCMC sampling, our theory immediately yields the last-iterate Wasserstein convergence of many advanced sampling schemes such as mirror Langevin, proximal, randomized mid-point, and Runge-Kutta methods.
Researcher Affiliation Academia Mohammad Reza Karimi ETH Zürich mkarimi@inf.ethz.ch Ya-Ping Hsieh ETH Zürich yaping.hsieh@inf.ethz.ch Andreas Krause ETH Zürich krausea@ethz.ch
Pseudocode No The paper describes algorithms using mathematical equations and descriptions (e.g., (LRM), (RMM), (ORMM)), but it does not provide any explicitly labeled pseudocode blocks or algorithms.
Open Source Code No The paper does not provide any statement or link indicating that open-source code for the described methodology is available.
Open Datasets No This is a theoretical paper and does not involve training on datasets. Therefore, it does not mention public datasets for training.
Dataset Splits No This is a theoretical paper and does not involve empirical experiments with data splits. Therefore, it does not provide training/test/validation dataset splits.
Hardware Specification No This is a theoretical paper and does not report on empirical experiments. Therefore, it does not describe the hardware used to run experiments.
Software Dependencies No This is a theoretical paper and does not report on empirical experiments. Therefore, it does not provide specific version numbers for software dependencies.
Experiment Setup No This is a theoretical paper and does not report on empirical experiments. Therefore, it does not provide details about an experimental setup, such as hyperparameters or training settings.