Blended Conditonal Gradients
Authors: Gábor Braun, Sebastian Pokutta, Dan Tu, Stephen Wright
ICML 2019 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Computational Experiments. We demonstrate the excellent computational behavior of BCG compared to other CG algorithms on standard problems, including video colocalization, sparse regression, structured SVM training, and structured regression. We observe significant computational speedups and in several cases empirically better convergence rates. We implemented Algorithm 1 as outlined above and used Si GD (Algorithm 2) for the descent steps as described in Section 4. For line search in Line 13 of Algorithm 2, we perform standard backtracking, and for Line 16 of Algorithm 1, we do ternary search. In Figure 1, each of the four plots itself contains four subplots depicting results of four variants of CG on a single instance. The two subplots in each upper row measure progress in the logarithm (to base 2) of the function value, while the two subplots in each lower row report the logarithm of the gap estimate Φt from Algorithm 1. The subplots in the left column of each plot report performance in terms of number of iterations, while the subplots in the right column report wall-clock time. |
| Researcher Affiliation | Academia | 1ISy E, Georgia Institute of Technology, Atlanta, GA 2Computer Sciences Department, University of Wisconsin, Madison, WI. |
| Pseudocode | Yes | Algorithm 1 Blended Conditional Gradients (BCG); Algorithm 2 Simplex Gradient Descent Step (Si GD) |
| Open Source Code | No | The paper does not provide an explicit statement about releasing the source code or a link to a code repository for the methodology described. |
| Open Datasets | No | The paper describes problems like 'Sparse signal recovery: minx Rn: x 1 τ y Φx 2 2, where Φ is of size 1000 3000 with density 0.05.' and 'Lasso. We solve minx P Ax b 2 with P being the (scaled) ℓ1-ball. A is a 400 2000 matrix with 100 non-zeros.' It mentions 'standard problems' and cites related work but does not provide specific links, DOIs, repository names, or formal citations with authors/year for the public access of the exact datasets or problem instances used. |
| Dataset Splits | No | The paper does not provide specific details on training, validation, or test dataset splits (e.g., percentages, sample counts, or citations to predefined splits). |
| Hardware Specification | No | The paper does not provide specific hardware details (e.g., exact GPU/CPU models, processor types, or memory amounts) used for running its experiments. |
| Software Dependencies | No | The paper mentions citing 'Gurobi Optimization. Gurobi optimizer reference manual version 6.5, 2016.' but does not specify other software dependencies like libraries or frameworks with version numbers for their own implementation. |
| Experiment Setup | No | The paper states: 'For line search in Line 13 of Algorithm 2, we perform standard backtracking, and for Line 16 of Algorithm 1, we do ternary search.' However, it lacks comprehensive specific experimental setup details such as hyperparameter values (e.g., learning rates, batch sizes, number of epochs) or optimizer settings. |