mlsanityData to 7 Oct 2026

Convergence Rate of Frank-Wolfe for Non-Convex Objectives

arXiv 1607.00345 ↗First posted 1 Jul 2016math.OC cs.LG cs.NAcited by 59

Not on the map. Why?

Abstract (arXiv)

We give a simple proof that the Frank-Wolfe algorithm obtains a stationary point at a rate of O(1/√t) on non-convex objectives with a Lipschitz continuous gradient. Our analysis is affine invariant and is the first, to the best of our knowledge, giving a similar rate to what was already proven for projected gradient methods (though on slightly different measures of stationarity).

Key facts. Cited by 59 papers in the map (data through 7 Oct 2026). First posted on arXiv 1 Jul 2016.

Builds on

No reference list yet.

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 10; 2022: 9; 2023: 9; 2024: 10; 2025: 10; 2026: 11.

59 papers.

Sort:

By area:

  1. 2024Chain of LoRA: Efficient Fine-tuning of Language Models via Residual Learningcited by 80
  2. 2025Lions and Muons: Optimization via Stochastic Frank-Wolfe under Heavy-Tailed Noisecited by 38
  3. 2021Online Graph Dictionary Learningcited by 37
  4. 2024Low-Rank Adaptation for Foundation Models: A Comprehensive Reviewcited by 35
  5. 2021Semi-relaxed Gromov-Wasserstein divergence with applications on graphscited by 21
  6. 2022Template based Graph Neural Network with Optimal Transport Distancescited by 20
  7. 2024C2M3: Cycle-Consistent Multi-Model Mergingcited by 20
  8. 2021Complexity of Linear Minimization and Projection on Some Setscited by 19
  9. 2021Escaping from Zero Gradient: Revisiting Action-Constrained Reinforcement Learning via Frank-Wolfe Policy Optimizationcited by 18
  10. 2022A Conditional Gradient-based Method for Simple Bilevel Optimization with Convex Lower-level Problemcited by 17
  11. 2023PPO-Clip Attains Global Optimality: Towards Deeper Understandings of Clippingcited by 17
  12. 2022Compression-aware Training of Neural Networks using Frank-Wolfecited by 16
38 more
  1. 2023Projection-Free Methods for Stochastic Simple Bilevel Optimization with Convex Lower-level Problemcited by 13
  2. 2024Distributional Reduction: Unifying Dimensionality Reduction and Clustering with Gromov-Wassersteincited by 12
  3. 2021Projection-Free Algorithm for Stochastic Bi-level Optimizationcited by 8
  4. 2022Curriculum-based Asymmetric Multi-task Reinforcement Learningcited by 7
  5. 2026Non-Euclidean Gradient Descent Operates at the Edge of Stabilitycited by 7
  6. 2023Sarah Frank-Wolfe: Methods for Constrained Optimization with Best Rates and Practical Featurescited by 6
  7. 2024Boosting Gradient Ascent for Continuous DR-submodular Maximizationcited by 6
  8. 2021Interpretable Neural Networks with Frank-Wolfe: Sparse Relevance Maps and Relevance Orderingscited by 5
  9. 2023LeanVec: Searching vectors faster by making them fitcited by 5
  10. 2024Projected Forward Gradient-Guided Frank-Wolfe Algorithm via Variance Reductioncited by 5
  11. 2025FW-Merging: Scaling Model Merging with Frank-Wolfe Optimizationcited by 5
  12. 2021Distributionally Robust Optimization with Markovian Datacited by 4
  13. 2021Subspace Detours Meet Gromov-Wassersteincited by 4
  14. 2024Revisiting Counterfactual Regression through the Lens of Gromov-Wasserstein Information Bottleneckcited by 4
  15. 2022Frank-Wolfe-based Algorithms for Approximating Tyler's M-estimatorcited by 3
  16. 2023Difference of Submodular Minimization via DC Programmingcited by 3
  17. 2024Large-Scale Non-convex Stochastic Constrained Distributionally Robust Optimizationcited by 3
  18. 2022Minimizing low-rank models of high-order tensors: Hardness, span, tight relaxation, and applicationscited by 2
  19. 2023Linearization Algorithms for Fully Composite Optimizationcited by 2
  20. 2023Power Control with QoS Guarantees: A Differentiable Projection-based Unsupervised Learning Frameworkcited by 2
  21. 2024Projection-Free Variance Reduction Methods for Stochastic Constrained Multi-Level Compositional Optimizationcited by 2
  22. 2025Revisiting Frank-Wolfe for Structured Nonconvex Optimizationcited by 2
  23. 2026Efficient Test-Time Finetuning of LLMs via Convex Reconstruction and Gradient Cachingcited by 2
  24. 2026BLADE: Scalable Bi-level Adaptive Data Selection for LLM Trainingcited by 2
  25. 2021A Regularized Wasserstein Framework for Graph Kernelscited by 1
  26. 2022Fast and Provably Convergent Algorithms for Gromov-Wasserstein in Graph Datacited by 1
  27. 2022SAIF: Sparse Adversarial and Imperceptible Attack Frameworkcited by 1
  28. 2023Leveraging Optimal Transport via Projections on Subspaces for Machine Learning Applicationscited by 1
  29. 2025Double-Bounded Nonlinear Optimal Transport for Size Constrained Min Cut Clusterincited by 1
  30. 2025An Efficient Local Search Approach for Polarized Community Discovery in Signed Networkscited by 1
  31. 2025MOSIC: Model-Agnostic Optimal Subgroup Identification with Multi-Constraint for Improved Reliabilitycited by 1
  32. 2025Scalable DC Optimization via Adaptive Frank-Wolfe Algorithmscited by 1
  33. 2025Don't Be Greedy, Just Relax! Pruning LLMs via Frank-Wolfecited by 1
  34. 2026Provably Efficient Algorithms for S- and Non-Rectangular Robust MDPs with General Parameterizationcited by 1
  35. 2026Principled and Scalable Diversity-Aware Retrieval via Cardinality-Constrained Binary Quadratic Programmingcited by 1
  36. 2021Scalable Projection-Free Optimizationcited by 0
  37. 2022Using Taylor-Approximated Gradients to Improve the Frank-Wolfe Method for Empirical Risk Minimizationcited by 0
  38. 2023Robust Graph Matching Using An Unbalanced Hierarchical Optimal Transport Frameworkcited by 0

50 most cited of 59 All 59 (JSON)