# Self-Concordant Analysis of Frank-Wolfe Algorithms

arXiv: https://arxiv.org/abs/2002.04320 · HTML: https://mlsanity.com/paper/2002.04320/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Feb 2020.

## Built on by (most cited first, 8 of 8)

- [Demystifying and Generalizing BinaryConnect](https://mlsanity.com/paper/2110.13220/) (2021)
- [Almost Free: Self-concordance in Natural Exponential Families and an Application to Bandits](https://mlsanity.com/paper/2410.01112/) (2024)
- [Parameter-free Locally Accelerated Conditional Gradients](https://mlsanity.com/paper/2102.06806/) (2021)
- [First-Order Methods for Convex Optimization](https://mlsanity.com/paper/2101.00935/) (2021)
- [Frank-Wolfe-based Algorithms for Approximating Tyler's M-estimator](https://mlsanity.com/paper/2206.09370/) (2022)
- [Scalable Frank-Wolfe on Generalized Self-concordant Functions via Simple Steps](https://mlsanity.com/paper/2105.13913/) (2021)
- [Faster Stochastic First-Order Method for Maximum-Likelihood Quantum State Tomography](https://mlsanity.com/paper/2211.12880/) (2022)
- [A conditional gradient homotopy method with applications to Semidefinite Programming](https://mlsanity.com/paper/2207.03101/) (2022)

## Abstract (arXiv)

Projection-free optimization via different variants of the Frank-Wolfe (FW), a.k.a. Conditional Gradient method has become one of the cornerstones in optimization for machine learning since in many cases the linear minimization oracle is much cheaper to implement than projections and some sparsity needs to be preserved. In a number of applications, e.g. Poisson inverse problems or quantum state tomography, the loss is given by a self-concordant (SC) function having unbounded curvature, implying absence of theoretical guarantees for the existing FW methods. We use the theory of SC functions to provide a new adaptive step size for FW methods and prove global convergence rate O(1/k) after k iterations. If the problem admits a stronger local linear minimization oracle, we construct a novel FW method with linear convergence rate for SC functions.