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We study the convergence properties of the 'greedy' Frank-Wolfe algorithm with a unit step size, for a convex maximization problem over a compact set. We assume the function satisfies smoothness and strong convexity. These assumptions…

Optimization and Control · Mathematics 2025-05-02 Fatih Selim Aktas , Christian Kroer

This paper studies first-order algorithms for solving fully composite optimization problems over convex and compact sets. We leverage the structure of the objective by handling its differentiable and non-differentiable components…

Optimization and Control · Mathematics 2023-07-13 Maria-Luiza Vladarean , Nikita Doikov , Martin Jaggi , Nicolas Flammarion

An extension of the Frank-Wolfe Algorithm (FWA), also known as Conditional Gradient algorithm, is proposed. In its standard form, the FWA allows to solve constrained optimization problems involving $\beta$-smooth cost functions, calling at…

Optimization and Control · Mathematics 2024-03-28 Guilherme Mazanti , Thibault Moquet , Laurent Pfeiffer

We give a simple and natural method for computing approximately optimal solutions for minimizing a convex function $f$ over a convex set $K$ given by a separation oracle. Our method utilizes the Frank--Wolfe algorithm over the cone of valid…

Optimization and Control · Mathematics 2022-03-14 Daniel Dadush , Christopher Hojny , Sophie Huiberts , Stefan Weltge

We derive global convergence bounds for the Frank Wolfe algorithm when training one hidden layer neural networks. When using the ReLU activation function, and under tractable preconditioning assumptions on the sample data set, the linear…

Optimization and Control · Mathematics 2020-02-07 Alexandre d'Aspremont , Mert Pilanci

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 presents a subgradient-based algorithm for constrained nonsmooth convex optimization that does not require projections onto the feasible set. While the well-established Frank-Wolfe algorithm and its variants already avoid…

Optimization and Control · Mathematics 2024-09-04 Kamiar Asgari , Michael J. Neely

We consider the problem of bandit optimization, inspired by stochastic optimization and online learning problems with bandit feedback. In this problem, the objective is to minimize a global loss function of all the actions, not necessarily…

Machine Learning · Computer Science 2017-09-07 Quentin Berthet , Vianney Perchet

With increasingly "big" data available in biomedical research, deriving accurate and reproducible biology knowledge from such big data imposes enormous computational challenges. In this paper, motivated by recently developed stochastic…

Computational Engineering, Finance, and Science · Computer Science 2015-05-27 Yijie Wang , Xiaoning Qian

Symmetric nonnegative matrix factorization has found abundant applications in various domains by providing a symmetric low-rank decomposition of nonnegative matrices. In this paper we propose a Frank-Wolfe (FW) solver to optimize the…

Machine Learning · Computer Science 2018-06-27 Han Zhao , Geoff Gordon

We tackle robust optimization problems under objective uncertainty in the oracle model, i.e., when the deterministic problem is solved by an oracle. The oracle-based setup is favorable in many situations, e.g., when a compact formulation of…

Optimization and Control · Mathematics 2024-12-06 Mathieu Besançon , Jannis Kurtz

We consider two greedy algorithms for minimizing a convex function in a bounded convex set: an algorithm by Jones [1992] and the Frank-Wolfe (FW) algorithm. We first consider approximate versions of these algorithms. For smooth convex…

Optimization and Control · Mathematics 2018-11-19 Nan Ye , Peter Bartlett

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

This paper studies the empirical efficacy and benefits of using projection-free first-order methods in the form of Conditional Gradients, a.k.a. Frank-Wolfe methods, for training Neural Networks with constrained parameters. We draw…

Machine Learning · Computer Science 2020-10-22 Sebastian Pokutta , Christoph Spiegel , Max Zimmer

The Frank-Wolfe (FW) algorithm has been widely used in solving nuclear norm constrained problems, since it does not require projections. However, FW often yields high rank intermediate iterates, which can be very expensive in time and space…

Machine Learning · Statistics 2017-10-17 Edward Cheung , Yuying Li

We propose a novel and efficient training method for RNNs by iteratively seeking a local minima on the loss surface within a small region, and leverage this directional vector for the update, in an outer-loop. We propose to utilize the…

Machine Learning · Computer Science 2020-10-16 Yun Yue , Ming Li , Venkatesh Saligrama , Ziming Zhang

We provide a template to derive convergence rates for the following popular versions of the Frank-Wolfe algorithm on polytopes: vanilla Frank-Wolfe, Frank-Wolfe with away steps, Frank-Wolfe with blended pairwise steps, and Frank-Wolfe with…

Optimization and Control · Mathematics 2025-05-21 Elias Wirth , Javier Pena , Sebastian Pokutta

We investigate the robustness of the Frank-Wolfe method when gradients are computed inexactly and examine the relative computational cost of the linear minimization oracle (LMO) versus projection. For smooth nonconvex functions, we…

Optimization and Control · Mathematics 2026-01-27 Tao Hu

It is known that the Frank-Wolfe (FW) algorithm, which is affine-covariant, enjoys accelerated convergence rates when the constraint set is strongly convex. However, these results rely on norm-dependent assumptions, usually incurring…

Optimization and Control · Mathematics 2020-11-09 Thomas Kerdreux , Lewis Liu , Simon Lacoste-Julien , Damien Scieur

Projection-free optimization algorithms, which are mostly based on the classical Frank-Wolfe method, have gained significant interest in the machine learning community in recent years due to their ability to handle convex constraints that…

Machine Learning · Computer Science 2021-02-24 Dan Garber , Ben Kretzu