Rapid Convergence of the Unadjusted Langevin Algorithm: Isoperimetry Suffices
Authors: Santosh Vempala, Andre Wibisono
NeurIPS 2019 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | We prove a convergence guarantee in Kullback Leibler (KL) divergence assuming satisfies log-Sobolev inequality and f has bounded Hessian. Notably, we do not assume convexity or bounds on higher derivatives. We also prove convergence guarantees in Rényi divergence of order q > 1 assuming the limit of ULA satisfies either log-Sobolev or Poincaré inequality. |
| Researcher Affiliation | Academia | Santosh S. Vempala College of Computing Georgia Institute of Technology Atlanta, GA 30332 vempala@gatech.edu Andre Wibisono College of Computing Georgia Institute of Technology Atlanta, GA 30332 wibisono@gatech.edu |
| Pseudocode | No | The paper describes the ULA algorithm by formula (xk+1 = xk rf(xk) + 2 zk) but does not present it in a formal pseudocode block or algorithm listing. |
| Open Source Code | No | The paper does not contain any statements about making source code publicly available or provide links to code repositories. |
| Open Datasets | No | The paper is theoretical and does not conduct experiments involving datasets for training. It discusses probability distributions conceptually but does not use them as empirical datasets. |
| Dataset Splits | No | The paper is theoretical and does not involve empirical validation on datasets, therefore no validation splits are mentioned. |
| Hardware Specification | No | The paper is theoretical and does not describe any experimental setup that would require hardware specifications. |
| Software Dependencies | No | The paper is theoretical and does not describe any experimental setup that would require specific software dependencies with version numbers. |
| Experiment Setup | No | The paper is theoretical and focuses on mathematical proofs and analysis rather than empirical experiments, thus it does not include details on an experimental setup or hyperparameters. |