On the Curved Geometry of Accelerated Optimization
Authors: Aaron Defazio
NeurIPS 2019 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | In this work we propose a differential geometric motivation for Nesterov s accelerated gradient method (AGM) for strongly-convex problems. By considering the optimization procedure as occurring on a Riemannian manifold with a natural structure, The AGM method can be seen as the proximal point method applied in this curved space. This viewpoint can also be extended to the continuous time case, where the accelerated gradient method arises from the natural block-implicit Euler discretization of an ODE on the manifold. We provide an analysis of the convergence rate of this ODE for quadratic objectives. |
| Researcher Affiliation | Industry | Aaron Defazio Facebook AI Research New York |
| Pseudocode | No | The paper does not contain structured pseudocode or algorithm blocks. Table 1 lists different forms of Nesterov's method with equations, but not in a pseudocode format. |
| Open Source Code | No | The paper does not provide any concrete access to source code for the methodology described. |
| Open Datasets | No | The paper is theoretical and does not use or refer to any publicly available datasets. |
| Dataset Splits | No | The paper is theoretical and does not involve dataset splits for training, validation, or testing. |
| Hardware Specification | No | The paper is theoretical and does not mention any hardware specifications used for experiments. |
| Software Dependencies | No | The paper is theoretical and does not list any specific software dependencies with version numbers. |
| Experiment Setup | No | The paper is theoretical and does not describe an experimental setup with hyperparameters or training configurations. |