No-regret Online Learning over Riemannian Manifolds
Authors: Xi Wang, Zhipeng Tu, Yiguang Hong, Yingyi Wu, Guodong Shi
NeurIPS 2021 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | 5 Numerical Experiment We validate our findings on Riemannian manifolds in both g-convex and strongly g-convex losses. We also compare our results with the Riemannian zeroth online (R-OZO) algorithm [29] if possible (the R-OZO is only suitable for strongly g-convex cases). All experiments are performed with the help of Pymanopt toolbox [34]2 on a 64 bit Windows platform with a 3.4 GHz CPU (AMD Ryzen5 2600) and the code used for the numerical experiments is provided in the supplementary materials. |
| Researcher Affiliation | Academia | Xi Wang AMSS Chinese Academy of Sciences Beijing, China wangxi14@mails.ucas.ac.cn Zhipeng Tu AMSS Chinese Academy of Sciences Beijing, China tuzhipeng@amss.ac.cn Yiguang Hong Tongji University Shanghai, China yghong@iss.ac.cn Yingyi Wu University of Chinese Academy of Sciences Beijing, China wuyy@ucas.ac.cn Guodong Shi The University of Sydney NSW, Australia guodong.shi@sydney.edu.au |
| Pseudocode | Yes | Algorithm 1: Riemannian Online Gradient Descent Algorithm (R-OGD) Algorithm 2: Riemannian Bandit Algorithm (R-BAN) |
| Open Source Code | Yes | All experiments are performed with the help of Pymanopt toolbox [34]2 on a 64 bit Windows platform with a 3.4 GHz CPU (AMD Ryzen5 2600) and the code used for the numerical experiments is provided in the supplementary materials. |
| Open Datasets | No | The data used for experiments is generated by the authors. For instance, in Section 5.1, it states: "Matrices Ai,t are randomly generated by the method in Pymanopt toolbox." and "The data Ai,t is randomly generated by normal Gaussian distributions." No concrete access information for publicly available datasets is provided. |
| Dataset Splits | No | The paper describes online learning where data is generated sequentially, not from a fixed dataset with predefined splits. Therefore, it does not mention training, validation, or test dataset splits. |
| Hardware Specification | Yes | All experiments are performed with the help of Pymanopt toolbox [34]2 on a 64 bit Windows platform with a 3.4 GHz CPU (AMD Ryzen5 2600) and the code used for the numerical experiments is provided in the supplementary materials. |
| Software Dependencies | No | The paper mentions using 'Pymanopt toolbox' but does not specify a version number for it or any other software dependencies. |
| Experiment Setup | Yes | Consider the case [n, N, T] = [100, 10, 10000] and set δ = 0.399 (which is four times the theoretical value) and α = 0.006. We test the R-OGD with with taking the Lipschitz constant L = 2 and test the R-BAN with δ = 0.22 (which is five times the theoretical value) and α = 0.002 for 100 different runs. |