Spectral Frank-Wolfe Algorithm: Strict Complementarity and Linear Convergence
Authors: Lijun Ding, Yingjie Fei, Qiantong Xu, Chengrun Yang
ICML 2020 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | 5. Numerics In this section, we verify numerically a few of our claims in the paper, and show the advantages of the Spectral Frank Wolfe algorithm when strict complementarity is satisfied and the solution rank is larger than 1. We focus on the quadratic sensing problem (Chen et al., 2015). Given a random matrix U Rn r with r = 3 and Frobenius norm U 2 F = 1, we generate Gaussian vectors ai Rn 1, i = 1, . . . , m and construct quadratic measurement vectors y0(i) = U ai 2 F, i = 1, . . . , m. [...] We set m = 15nr in all our experiments. [...] We compare the performance of FW, G-Block FW, and Spec FW. [...] We plot the relative objective value against both the time and iteration counter in Figure 1. |
| Researcher Affiliation | Collaboration | 1School of ORIE, Cornell University, Ithaca, NY 14850, USA 2Facebook AI Research, Menlo Park, CA 94025, USA 3School of Electrical and Computer Engineering, Cornell University, Ithaca, NY 14850, USA. |
| Pseudocode | Yes | Algorithm 1 Frank-Wolfe with line search |
| Open Source Code | No | The paper mentions using FASTA for solving SDP but does not provide any explicit statement or link to open-source code for its own proposed methodology. |
| Open Datasets | No | We focus on the quadratic sensing problem (Chen et al., 2015). Given a random matrix U Rn r with r = 3 and Frobenius norm U 2 F = 1, we generate Gaussian vectors ai Rn 1, i = 1, . . . , m and construct quadratic measurement vectors y0(i) = U ai 2 F, i = 1, . . . , m. |
| Dataset Splits | No | The paper specifies parameters for data generation and experimental settings (e.g., 'We set m = 15nr in all our experiments'), but it does not detail specific training, validation, or test dataset splits or percentages. |
| Hardware Specification | No | The paper does not provide specific hardware details (e.g., CPU/GPU models, memory) used for running its experiments. |
| Software Dependencies | No | The small-scale SDP (10) is solved via FASTA (Goldstein et al., 2014; 2015). |
| Experiment Setup | Yes | We set m = 15nr in all our experiments. [...] We set c = 0.5 for the noise Level. We also set τ = 0.5 [...] We set k = 4 for both Spec FW and G-Block FW, which is larger than r = 3. We also set η = 0.4 and β = 2.5n2. |