Convergence and Trade-Offs in Riemannian Gradient Descent and Riemannian Proximal Point
Authors: David Martı́nez-Rubio, Christophe Roux, Sebastian Pokutta
ICML 2024 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Further, we explore beyond our theory with empirical tests. ... 5. Experiments: Numerical tests exploring beyond our theory. We observe that RGD presents a monotonic decrease in distance to an optimizer and show that RIPPA is competitive. |
| Researcher Affiliation | Academia | 1Zuse Institute Berlin, Germany 2Technische Universit at Berlin, Germany. |
| Pseudocode | Yes | Algorithm 1 Riemannian Inexact Proximal Point Algorithm (RIPPA) |
| Open Source Code | No | The paper mentions using the Pymanopt library (Townsend et al., 2016), published under the BSD-3-Clause license. This indicates the use of an open-source library, but the paper does not state that the authors are releasing their own code for the methodology described. |
| Open Datasets | No | The paper describes generating synthetic data ('centers yi') for the Karcher mean problem, but does not refer to a publicly available or open dataset with concrete access information (link, DOI, repository, or formal citation). |
| Dataset Splits | No | The paper describes a problem setup for the Karcher mean but does not provide specific details on training, validation, or test dataset splits. |
| Hardware Specification | No | The paper does not provide specific hardware details (exact GPU/CPU models, processor types, or detailed computer specifications) used for running its experiments. |
| Software Dependencies | No | The paper mentions using the 'Pymanopt library (Townsend et al., 2016)' but does not specify its version number or any other software dependencies with specific version numbers. |
| Experiment Setup | Yes | We implement RGD with step sizes η = 1/L and η = 1/(LζR) as well as RIPPA performing a constant number of iterations of PRGD to approximately solve the proximal problems. ... We performed 3 iterations in each subroutine. ... We run until a fixed precision is reached in function value, and because of this, different algorithms stop at points at different distances from x*. ... In fact, we ran the algorithms for different settings, different initializations, and we performed a grid search on the step sizes. |