Low-Rank Extragradient Method for Nonsmooth and Low-Rank Matrix Optimization Problems
Authors: Atara Kaplan, Dan Garber
NeurIPS 2021 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We present extensive numerical evidence that demonstrate both the plausibility of the GSC assumption in various tasks, and more importantly, demonstrate that indeed the extragradient method with simple initialization converges correctly (i.e., produces exactly the same sequences of iterates) when the rank of the SVDs used to compute the (truncated) projections matches the rank of the (low-rank) ground-truth matrix to be recovered, instead of naively using full-rank SVDs (as suggested by (2)). See Section 5. |
| Researcher Affiliation | Academia | Dan Garber Technion Israel Institute of Technology Haifa, Israel 3200003 dangar@technion.ac.il Atara Kaplan Technion Israel Institute of Technology Haifa, Israel 3200003 ataragold@campus.technion.ac.il |
| Pseudocode | Yes | Algorithm 1 Projected extragradient method for saddle-point problems (see also [23, 30]) |
| Open Source Code | No | The paper does not contain any explicit statement about releasing the source code for the methodology described, nor does it provide a link to a code repository. |
| Open Datasets | No | The paper states: 'For all tasks considered we generate random instances, and examine the sequences of iterates generated by Algorithm 1...' This indicates the data was generated for the experiments, not obtained from a publicly available dataset with a specific link or citation. |
| Dataset Splits | No | The paper states: 'For all tasks considered we generate random instances... and for any set of parameters we average the measurements over 10 i.i.d. runs.' While this describes part of the experimental procedure, it does not specify explicit training/validation/test dataset splits or cross-validation details for a given dataset. |
| Hardware Specification | No | The paper does not provide specific details about the hardware used for running experiments, such as CPU/GPU models, memory, or cloud instance types. |
| Software Dependencies | No | The paper does not provide specific version numbers for any software components, libraries, or solvers used in the experiments. |
| Experiment Setup | Yes | We initialize the X variable with the rank-one approximation of M. That is, we take X1 = u1u 1 , where u1 is the top eigenvector of M. For the Y variable we initialize it with Y1 = sign(X1) which is a subgradient of X1 1. We set the step-size to η = 1/(2λ) and we set the number of iterations to T = 1000 and for any set of parameters we average the measurements over 10 i.i.d. runs. |