Notice: The reproducibility variables underlying each score are classified using an automated LLM-based pipeline, validated against a manually labeled dataset. LLM-based classification introduces uncertainty and potential bias; scores should be interpreted as estimates. Full accuracy metrics and methodology are described in Coakley et alK. L. Coakley, T. Snelleman, H. Hoos, and O. E. Gundersen, "The embrace of open science: An analysis of a decade of AI research and 56 800 conference papers," Under Review, 2026..
Efficient Quadratic Corrections for Frank-Wolfe Algorithms
Authors: Jannis Halbey, Seta Rakotomandimby, Mathieu Besançon, Sébastien Designolle, Sebastian Pokutta
NeurIPS 2025 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | 4 ExperimentsIn this section, we present numerical experiments on two classical quadratic problems and on two applications of quadratic corrections to SCG and SOCGS. In all experiments, we use a hybrid of BPCG and QC steps, performing a QC step whenever N new atoms have been added to the active set. In the first two experiments, we compare QC-LP and QC-MNP with four baselines: FW, AFW, PFW, and BPCG. For SCG and SOCGS, we compare against the original used FW variant and BPCG, to demonstrate the effectiveness of the quadratic corrections. Additional details and further experiments are provided in Section F. All runs were executed on a cluster with Intel Xeon Gold 6338 CPUs at 2 GHz and 12 GB RAM, with time and iteration limits chosen according to problem size. |
| Researcher Affiliation | Academia | Jannis Halbey Zuse Institute Berlin & TU Berlin Berlin, Germany EMAIL Seta Rakotomandimby École nationale des ponts et chaussées, IP Paris Champs-sur-Marne, France EMAIL Mathieu Besançon Université Grenoble Alpes, Inria, LIG, CNRS Grenoble, France EMAIL Sébastien Designolle Zuse Institute Berlin Berlin, Germany EMAIL Sebastian Pokutta Zuse Institute Berlin & TU Berlin Berlin, Germany EMAIL |
| Pseudocode | Yes | Algorithm 1 Corrective Frank-Wolfe (CFW) Algorithm 2 Corrective Step CS(S, x, a, s) Algorithm 3 Local Pairwise Step LPS(S, x, a, s) Algorithm 4 Fully-Corrective Step FCS(S) Algorithm 5 Quadratic Correction LP Algorithm 6 Quadratic Correction MNP Algorithm 7 Lazified Corrective Frank-Wolfe (LCFW) Algorithm 8 Quadratic Correction MNP Algorithm 9 Split Conditional Gradient (SCG) Algorithm 10 Second-Order Conditional Gradient Sliding (SOCGS) Algorithm 11 Projected Variable-Metric (PVM) algorithm |
| Open Source Code | Yes | Justification: We provide the code for reproducing the experimental results in the supplemental material. |
| Open Datasets | Yes | We consider a family of 3x3 entangled states proposed in Horodecki [1997] The labels yi {-1, 1} and feature vectors zi Rn are taken from the gisette training dataset [Guyon et al., 2007] |
| Dataset Splits | No | The paper describes synthetic data generation ( |
| Hardware Specification | Yes | All runs were executed on a cluster with Intel Xeon Gold 6338 CPUs at 2 GHz and 12 GB RAM |
| Software Dependencies | No | For the actual implementation, we have used the Frank Wolfe.jl package [Besançon et al., 2022]. |
| Experiment Setup | Yes | We used a fixed interval length of N = 10 for the quadratic correction steps. We used a fixed interval length of N = 1 for QC-MNP and N = 10 for QC-LP. The results for n {300, 500} using c = 0.9, q = 0.1 and N = 1 are given in Figure 3. The results for k {50, 200} inner iterations are depicted in Figure 4. All methods follow an identical trajectory in the initial phase, indicating that SOCGS chooses only the outer step. Once the distance to the optimum is sufficiently small, the QC methods exhibit substantial improvements over BPCG in both instances. Further analysis reveals that QC-MNP and QC-LP perform more FW steps than BPCG on the inner problem by avoiding additional pairwise steps, which yields a drastic initial decrease in primal values and the FW gap. For longer runs of the inner problem, i.e., larger k, the acceleration of the QC methods is less pronounced, yielding a similar performance as AFW. The hybrid method with QC-MNP performs more quadratic corrections than QC-LP, yielding more significant acceleration but also longer runs in wall-clock time. |