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Related papers: A Novel Frank-Wolfe Algorithm. Analysis and Applic…

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We propose a semi-stochastic Frank-Wolfe algorithm with away-steps for regularized empirical risk minimization and extend it to problems with block-coordinate structure. Our algorithms use adaptive step-size and we show that they converge…

Optimization and Control · Mathematics 2016-02-16 Donald Goldfarb , Garud Iyengar , Chaoxu Zhou

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

We extend the Frank-Wolfe (FW) optimization algorithm to solve constrained smooth convex-concave saddle point (SP) problems. Remarkably, the method only requires access to linear minimization oracles. Leveraging recent advances in FW…

Optimization and Control · Mathematics 2017-03-07 Gauthier Gidel , Tony Jebara , Simon Lacoste-Julien

The analysis of Frank Wolfe (FW) variants is often complicated by the presence of different kinds of "good" and "bad" steps. In this article we aim to simplify the convergence analysis of some of these variants by getting rid of such a…

Optimization and Control · Mathematics 2022-11-22 Francesco Rinaldi , Damiano Zeffiro

The Frank-Wolfe method (a.k.a. conditional gradient algorithm) for smooth optimization has regained much interest in recent years in the context of large scale optimization and machine learning. A key advantage of the method is that it…

Optimization and Control · Mathematics 2015-08-17 Dan Garber , Elad Hazan

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

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 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

Training a Support Vector Machine (SVM) requires the solution of a quadratic programming problem (QP) whose computational complexity becomes prohibitively expensive for large scale datasets. Traditional optimization methods cannot be…

Machine Learning · Computer Science 2014-01-29 Emanuele Frandi , Ricardo Nanculef , Maria Grazia Gasparo , Stefano Lodi , Claudio Sartori

This paper considers stochastic convex optimization problems with two sets of constraints: (a) deterministic constraints on the domain of the optimization variable, which are difficult to project onto; and (b) deterministic or stochastic…

Optimization and Control · Mathematics 2022-05-25 Zeeshan Akhtar , Ketan Rajawat

Frank-Wolfe algorithms have recently regained the attention of the Machine Learning community. Their solid theoretical properties and sparsity guarantees make them a suitable choice for a wide range of problems in this field. In addition,…

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

We introduce novel techniques to enhance Frank-Wolfe algorithms by leveraging function smoothness beyond traditional short steps. Our study focuses on Frank-Wolfe algorithms with step sizes that incorporate primal-dual guarantees, offering…

Optimization and Control · Mathematics 2025-02-03 David Martínez-Rubio , Sebastian Pokutta

The stochastic Frank-Wolfe method has recently attracted much general interest in the context of optimization for statistical and machine learning due to its ability to work with a more general feasible region. However, there has been a…

Optimization and Control · Mathematics 2019-11-06 Haihao Lu , Robert M. Freund

This paper aims to enhance the use of the Frank-Wolfe (FW) algorithm for training deep neural networks. Similar to any gradient-based optimization algorithm, FW suffers from high computational and memory costs when computing gradients for…

Machine Learning · Computer Science 2024-12-30 M. Rostami , S. S. Kia

The Frank-Wolfe algorithm is a popular method for minimizing a smooth convex function $f$ over a compact convex set $\mathcal{C}$. While many convergence results have been derived in terms of function values, hardly nothing is known about…

Optimization and Control · Mathematics 2022-02-18 Jérôme Bolte , Cyrille W. Combettes , Édouard Pauwels

We present and analyze an away-step Frank-Wolfe method for the convex optimization problem ${\min}_{x\in\mathcal{X}} \; f(\mathsf{A} x) + \langle{c},{x}\rangle$, where $f$ is a $\theta$-logarithmically-homogeneous self-concordant barrier,…

Optimization and Control · Mathematics 2023-08-30 Renbo Zhao

This paper proposes a new variant of Frank-Wolfe (FW), called $k$FW. Standard FW suffers from slow convergence: iterates often zig-zag as update directions oscillate around extreme points of the constraint set. The new variant, $k$FW,…

Optimization and Control · Mathematics 2021-11-17 Lijun Ding , Jicong Fan , Madeleine Udell

We present a new Frank-Wolfe (FW) type algorithm that is applicable to minimization problems with a nonsmooth convex objective. We provide convergence bounds and show that the scheme yields so-called coreset results for various Machine…

Optimization and Control · Mathematics 2017-08-23 Sathya N. Ravi , Maxwell D. Collins , Vikas Singh

Multi-category support vector machine (MC-SVM) is one of the most popular machine learning algorithms. There are lots of variants of MC-SVM, although different optimization algorithms were developed for different learning machines. In this…

Machine Learning · Computer Science 2021-11-10 Kenya Tajima , Yoshihiro Hirohashi , Esmeraldo Ronnie Rey Zara , Tsuyoshi Kato

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