Notice: The reproducibility variables underlying each score are classified using an automated LLM-based pipeline, validated against a manually labeled dataset. LLM-based classification introduces uncertainty and potential bias; scores should be interpreted as estimates. Full accuracy metrics and methodology are described in Coakley et alK. L. Coakley, T. Snelleman, H. Hoos, and O. E. Gundersen, "The embrace of open science: An analysis of a decade of AI research and 56 800 conference papers," Under Review, 2026..
Necessary and Sufficient Geometries for Gradient Methods
Authors: Daniel Levy, John C. Duchi
NeurIPS 2019 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | We study the impact of the constraint set and gradient geometry on the convergence of online and stochastic methods for convex optimization, providing a characterization of the geometries for which stochastic gradient and adaptive gradient methods are (minimax) optimal. In particular, we show that when the constraint set is quadratically convex, diagonally pre-conditioned stochastic gradient methods are minimax optimal. We further provide a converse that shows that when the constraints are not quadratically convex for example, any p-ball for p < 2 the methods are far from optimal. Based on this, we can provide concrete recommendations for when one should use adaptive, mirror or stochastic gradient methods. |
| Researcher Affiliation | Academia | Daniel Levy Stanford University EMAIL John C. Duchi Stanford University EMAIL |
| Pseudocode | No | The paper describes algorithms mathematically (e.g., mirror descent updates), but does not include any pseudocode or algorithm blocks. |
| Open Source Code | No | The paper does not mention or provide access to any open-source code for the methodology described. |
| Open Datasets | No | This is a theoretical paper focused on mathematical proofs and analyses, not empirical studies involving datasets or training. Therefore, no information about publicly available training datasets is provided. |
| Dataset Splits | No | This is a theoretical paper and does not involve experimental validation with dataset splits. No specific dataset split information (percentages, sample counts, or citations to predefined splits) is provided. |
| Hardware Specification | No | This is a theoretical paper and does not describe any experiments that would require hardware. Therefore, no hardware specifications are provided. |
| Software Dependencies | No | This is a theoretical paper and does not mention any software dependencies with specific version numbers. |
| Experiment Setup | No | This is a theoretical paper that does not describe empirical experiments with hyperparameters or training configurations. Therefore, no experimental setup details are provided. |