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The paper introduces a new adaptive version of the Frank-Wolfe algorithm for relatively smooth convex functions. It is proposed to use the Bregman divergence other than half the square of the Euclidean norm in the formula for step-size.…

Optimization and Control · Mathematics 2024-07-23 Alexander Vyguzov , Fedor Stonyakin

Recently, there has been a renewed interest in the machine learning community for variants of a sparse greedy approximation procedure for concave optimization known as {the Frank-Wolfe (FW) method}. In particular, this procedure has been…

Computer Vision and Pattern Recognition · Computer Science 2015-10-27 Hector Allende , Emanuele Frandi , Ricardo Nanculef , Claudio Sartori

We develop a Frank-Wolfe algorithm with corrective steps, generalizing previous algorithms including blended conditional gradients, blended pairwise conditional gradients, and fully-corrective Frank-Wolfe. For this, we prove tight…

Optimization and Control · Mathematics 2026-05-21 Jannis Halbey , Seta Rakotomandimby , Mathieu Besançon , Sébastien Designolle , Sebastian Pokutta

The Frank-Wolfe (FW) method, which implements efficient linear oracles that minimize linear approximations of the objective function over a fixed compact convex set, has recently received much attention in the optimization and machine…

Optimization and Control · Mathematics 2024-01-19 Liaoyuan Zeng , Yongle Zhang , Guoyin Li , Ting Kei Pong , Xiaozhou Wang

Frank-Wolfe algorithm (FW) and its variants have gained a surge of interests in machine learning community due to its projection-free property. Recently people have reduced the gradient evaluation complexity of FW algorithm to…

Machine Learning · Statistics 2018-05-22 Yan Li , Chao Qu , Huan Xu

The Frank-Wolfe (FW) method is a popular algorithm for solving large-scale convex optimization problems appearing in structured statistical learning. However, the traditional Frank-Wolfe method can only be applied when the feasible region…

Optimization and Control · Mathematics 2021-10-11 Haoyue Wang , Haihao Lu , Rahul Mazumder

The Frank-Wolfe algorithm achieves a convergence rate of $\mathcal{O}(1/T)$ for smooth convex optimization over compact convex domains, accelerating to $\mathcal{O}(1/T^2)$ when both the objective and the feasible set are strongly convex.…

Optimization and Control · Mathematics 2026-05-19 Jannis Halbey , Christophe Roux , Sebastian Pokutta

We propose a rank-$k$ variant of the classical Frank-Wolfe algorithm to solve convex optimization over a trace-norm ball. Our algorithm replaces the top singular-vector computation ($1$-SVD) in Frank-Wolfe with a top-$k$ singular-vector…

Machine Learning · Computer Science 2017-11-10 Zeyuan Allen-Zhu , Elad Hazan , Wei Hu , Yuanzhi Li

The Conditional Gradient (or Frank-Wolfe) method is one of the most well-known methods for solving constrained optimization problems appearing in various machine learning tasks. The simplicity of iteration and applicability to many…

Optimization and Control · Mathematics 2024-09-17 Ruslan Nazykov , Aleksandr Shestakov , Vladimir Solodkin , Aleksandr Beznosikov , Gauthier Gidel , Alexander Gasnikov

We propose a novel generalization of the conditional gradient (CG / Frank-Wolfe) algorithm for minimizing a smooth function $f$ under an intersection of compact convex sets, using a first-order oracle for $\nabla f$ and linear minimization…

Optimization and Control · Mathematics 2024-10-11 Zev Woodstock , Sebastian Pokutta

A broad class of convex optimization problems can be formulated as a semidefinite program (SDP), minimization of a convex function over the positive-semidefinite cone subject to some affine constraints. The majority of classical SDP solvers…

Optimization and Control · Mathematics 2019-10-30 Francesco Locatello , Alp Yurtsever , Olivier Fercoq , Volkan Cevher

The Frank-Wolfe method has become increasingly useful in statistical and machine learning applications, due to the structure-inducing properties of the iterates, and especially in settings where linear minimization over the feasible set is…

Machine Learning · Computer Science 2024-12-16 Zikai Xiong , Robert M. Freund

Frank-Wolfe (FW) algorithms have been often proposed over the last few years as efficient solvers for a variety of optimization problems arising in the field of Machine Learning. The ability to work with cheap projection-free iterations and…

Machine Learning · Statistics 2015-10-27 Emanuele Frandi , Ricardo Nanculef , Stefano Lodi , Claudio Sartori , Johan A. K. Suykens

The Frank-Wolfe algorithm is a popular method in structurally constrained machine learning applications, due to its fast per-iteration complexity. However, one major limitation of the method is a slow rate of convergence that is difficult…

Optimization and Control · Mathematics 2023-04-14 Zhaoyue Chen , Yifan Sun

Recent papers have shown that the Frank-Wolfe algorithm (FW) with open-loop step-sizes exhibits rates of convergence faster than the iconic $\mathcal{O}(t^{-1})$ rate. In particular, when the minimizer of a strongly convex function over a…

Optimization and Control · Mathematics 2025-01-22 Elias Wirth , Javier Pena , Sebastian Pokutta

The Frank-Wolfe method is a popular method in sparse constrained optimization, due to its fast per-iteration complexity. However, the tradeoff is that its worst case global convergence is comparatively slow, and importantly, is…

Optimization and Control · Mathematics 2022-05-25 Zhaoyue Chen , Yifan Sun

The Frank-Wolfe algorithm, a very first optimization method and also known as the conditional gradient method, was introduced by Frank and Wolfe in 1956. Due to its simple linear subproblems, the Frank-Wolfe algorithm has recently been…

Optimization and Control · Mathematics 2017-10-23 Hong-Kun Xu

The Frank-Wolfe optimization algorithm has recently regained popularity for machine learning applications due to its projection-free property and its ability to handle structured constraints. However, in the stochastic learning setting, it…

Machine Learning · Computer Science 2017-09-15 Elad Hazan , Haipeng Luo

We consider the oracle complexity of constrained convex optimization given access to a Linear Minimization Oracle (LMO) for the constraint set and a gradient oracle for the $L$-smooth, strongly convex objective. This model includes…

Optimization and Control · Mathematics 2026-02-27 Benjamin Grimmer , Ning Liu

We propose an enhanced zeroth-order stochastic Frank-Wolfe framework to address constrained finite-sum optimization problems, a structure prevalent in large-scale machine-learning applications. Our method introduces a novel double variance…

Machine Learning · Computer Science 2025-01-24 Haishan Ye , Yinghui Huang , Hao Di , Xiangyu Chang