Integration Methods and Optimization Algorithms
Authors: Damien Scieur, Vincent Roulet, Francis Bach, Alexandre d'Aspremont
NeurIPS 2017 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | We show that accelerated optimization methods can be seen as particular instances of multi-step integration schemes from numerical analysis, applied to the gradient flow equation. Compared with recent advances in this vein, the differential equation considered here is the basic gradient flow, and we derive a class of multi-step schemes which includes accelerated algorithms, using classical conditions from numerical analysis. A full analysis is carried out for linear gradient flows (quadratic optimization) and provides compelling explanations for the acceleration phenomenon. |
| Researcher Affiliation | Academia | Damien Scieur INRIA, ENS, PSL Research University, Paris France damien.scieur@inria.fr Vincent Roulet INRIA, ENS, PSL Research University, Paris France vincent.roulet@inria.fr Francis Bach INRIA, ENS, PSL Research University, Paris France francis.bach@inria.fr Alexandre d Aspremont CNRS, ENS PSL Research University, Paris France aspremon@ens.fr |
| Pseudocode | No | The paper describes methods through mathematical equations and text, but does not include any structured pseudocode or algorithm blocks. |
| Open Source Code | No | The paper does not provide any specific links to code repositories or explicit statements about code availability. |
| Open Datasets | No | The paper focuses on theoretical analysis and numerical simulations of mathematical models (e.g., linear ODE, quadratic functions) rather than using named empirical datasets. |
| Dataset Splits | No | The paper does not use empirical datasets and therefore does not provide specific information regarding training, validation, or test dataset splits. |
| Hardware Specification | No | The paper does not provide any specific hardware details (e.g., GPU/CPU models, processor types, memory amounts) used for running its simulations or analysis. |
| Software Dependencies | No | The paper does not provide specific ancillary software details, such as library names with version numbers, needed to replicate any simulations. |
| Experiment Setup | No | The paper does not provide specific experimental setup details such as concrete hyperparameter values or training configurations, as its focus is theoretical analysis and mathematical derivation. |