Secant Line Search for Frank-Wolfe Algorithms
Authors: Deborah Hendrych, Sebastian Pokutta, Mathieu Besançon, David Martı́nez-Rubio
ICML 2025 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We provide theoretical guarantees and demonstrate the effectiveness of the strategy through numerical experiments. Numerical experiments. We provide extensive numerical experiments demonstrating the superior computational performance of SLS over other step sizes. |
| Researcher Affiliation | Academia | 1Zuse Institute Berlin, Berlin, Germany 2Berlin Institute of Technology, Berlin, Germany 3Université Grenoble Alpes, Inria, Laboratoire d Informatique de Grenoble, Grenoble, France 4Signal Theory and Communications Department, Carlos III University of Madrid, Madrid, Spain. |
| Pseudocode | Yes | Algorithm 1 Frank-Wolfe algorithm (Frank & Wolfe, 1956; Levitin & Polyak, 1966) [...] Algorithm 2 Secant Line Search (SLS) |
| Open Source Code | Yes | The implementation of the experiments was done with the Julia package Frank Wolfe.jl and is available as part of the package. |
| Open Datasets | Yes | The instances are taken from Carderera et al. (2024) and denoted by Port . |
| Dataset Splits | No | The paper does not explicitly provide specific dataset split percentages, sample counts for each split, or detailed methodology for creating splits (e.g., random seed for splitting). |
| Hardware Specification | No | The paper does not provide specific hardware details (e.g., GPU/CPU models, memory, or cloud instance types) used for running the experiments. It only mentions that experiments are carried out in Julia. |
| Software Dependencies | Yes | All experiments are carried out in Julia with the blended pairwise FW variant implemented in Frank Wolfe.jl (Besançon et al., 2022; 2025) |
| Experiment Setup | Yes | All experiments are carried out in Julia with the blended pairwise FW variant implemented in Frank Wolfe.jl (Besançon et al., 2022; 2025) with default parameters and a one-hour time limit. An instance is considered solved if the FW gap reaches 10 7. Algorithm 2 Secant Line Search (SLS) 1: Input: Function f, initial point xt, direction dt, initial step sizes γ0, γ1, tolerance ϵ [...] with SLS initialized with γ0 = 0 and γ1 = γ0+ρ, where ρ is a small positive perturbation [...] Both methods were run with the same initial step size γ0 = 0 and γ1 = γ0 + ρ with ρ = 10 5 and to the target accuracy of 10 8. |