Stochastic Conditional Gradient Methods: From Convex Minimization to Submodular Maximization
Authors: Aryan Mokhtari, Hamed Hassani, Amin Karbasi
JMLR 2020 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | 6. Numerical Experiments In this section, we compare the performances of the proposed stochastic conditional gradient method with state-of-the-art algorithms in both convex and submodular settings. 6.1. Convex Setting We first compare the proposed SFW algorithm and mini-batch FW for a stochastic quadratic program of the form (2). Then, we compare their performances in solving a matrix completion problem. In this section, by mini-batch FW we refer to a variant of FW that simply replaces gradients by a mini-batch of stochastic gradients. |
| Researcher Affiliation | Academia | Aryan Mokhtari EMAIL Department of Electrical and Computer Engineering The University of Texas at Austin Austin, TX 78712 Hamed Hassani EMAIL Department of Electrical and Systems Engineering University of Pennsylvania Philadelphia, PA 19104 Amin Karbasi EMAIL Department of Electrical Engineering and Computer Science Yale University New Haven, CT 06520 |
| Pseudocode | Yes | Algorithm 1 Stochastic Frank-Wolfe (SFW) ... Algorithm 2 Stochastic Continuous Greedy (SCG) ... Algorithm 3 Non-monotone Stochastic Continuous Greedy (NMSCG) |
| Open Source Code | No | The paper does not contain any explicit statements or links indicating that source code for the described methodology is publicly available. The license information provided relates to the paper itself, not its accompanying code. |
| Open Datasets | Yes | To run the experiments we use the Movie Lens data set. It consists of 1 million ratings (from 1 to 5) by N = 6041 users for n = 4000 movies. |
| Dataset Splits | No | The paper mentions using the Movie Lens data set, stating it consists of '1 million ratings (from 1 to 5) by N = 6041 users for n = 4000 movies.' However, it does not provide specific details on how this dataset was split into training, testing, or validation sets for the experiments. |
| Hardware Specification | No | The paper does not provide specific hardware details (e.g., CPU, GPU models, or memory specifications) used for running its experiments. |
| Software Dependencies | No | The paper does not provide specific software dependencies or version numbers (e.g., library names with version numbers) needed to replicate the experiments. |
| Experiment Setup | Yes | In our experiments, we set the dimension of the problem to n = 5 and the lower bound and upper bounds for the set C to l = 10 and u = 100. ... for the cases that the total number of iterations is T = {100, 200, 400, 800, 1600, 3200, 6400, 12800}. We further illustrates the performance of the (deterministic) FW as a benchmark. ... with batch sizes b = {1, 10, 50} ... The stepsize for all the three algorithms is γt = 1/(t+1) and the averaging parameter for our proposed SFW algorithm is ρt = 1/(t+1)2/3. ... In our experiments, we set the rank to r = 10 and the bound on the nuclear norm to α = ˆX |