A Lyapunov Analysis of Accelerated Methods in Optimization
Authors: Ashia C. Wilson, Ben Recht, Michael I. Jordan
JMLR 2021 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | We show there is an equivalence between the technique of estimate sequences and a family of Lyapunov functions in both continuous and discrete time. This connection allows us to develop a unified analysis of many existing accelerated algorithms, introduce new algorithms, and strengthen the connection between accelerated algorithms and continuous-time dynamical systems. |
| Researcher Affiliation | Academia | Ashia C. Wilson EMAIL Department of Electrical Engineering and Computer Sciences Massachusetts Instituted of Technology Cambridge, MA, 02139, USA Ben Recht EMAIL Department of Electrical Engineering and Computer Sciences University of California Berkeley, CA 94720-1776, USA Michael I. Jordan EMAIL Department of Electrical Engineering and Computer Sciences Department of Statistics University of California Berkeley, CA 94720-1776, USA |
| Pseudocode | Yes | Written as an algorithm, the implicit Euler method applied to (17b) and (17a) has the following update equations: zk+1 = arg min z X n Akf(x) + 1 δτk Dh (z, zk) o , (18a) xk+1 = δτk 1+δτk zk+1 + 1 1+δτk xk, (18b) |
| Open Source Code | No | The information is insufficient. The paper does not provide any statements about releasing its own source code, nor does it include a link to a code repository. Mentions of code refer to external work or are part of theoretical algorithm descriptions. |
| Open Datasets | No | The information is insufficient. The paper is purely theoretical and does not conduct experiments involving datasets. |
| Dataset Splits | No | The information is insufficient. The paper is theoretical and does not perform experiments that would require dataset splits. |
| Hardware Specification | No | The information is insufficient. The paper focuses on theoretical analysis and does not describe any experimental setup involving specific hardware. |
| Software Dependencies | No | The information is insufficient. The paper is theoretical and does not detail software dependencies with version numbers, as it does not report on computational experiments. |
| Experiment Setup | No | The information is insufficient. The paper is theoretical and does not describe any experimental setup, hyperparameters, or training configurations. |