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Related papers: Avoiding bad steps in Frank Wolfe variants

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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 study the Frank-Wolfe algorithm for constrained optimization problems with relatively smooth objectives. Building upon our previous work, we propose a fully adaptive variant of the Frank-Wolfe method that dynamically adjusts the step…

Optimization and Control · Mathematics 2025-08-27 A. A. Vyguzov , F. S. Stonyakin

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

Error bound condition has recently gained revived interest in optimization. It has been leveraged to derive faster convergence for many popular algorithms, including subgradient methods, proximal gradient method and accelerated proximal…

Optimization and Control · Mathematics 2018-10-12 Yi Xu , Tianbao Yang

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

We introduce a few variants on Frank-Wolfe style algorithms suitable for large scale optimization. We show how to modify the standard Frank-Wolfe algorithm using stochastic gradients, approximate subproblem solutions, and sketched decision…

Optimization and Control · Mathematics 2018-08-17 Lijun Ding , Madeleine Udell

The Frank Wolfe algorithm (FW) is a popular projection-free alternative for solving large-scale constrained optimization problems. However, the FW algorithm suffers from a sublinear convergence rate when minimizing a smooth convex function…

Optimization and Control · Mathematics 2021-10-20 Robin Francis , Sundeep Prabhakar Chepuri

Generalized self-concordance is a key property present in the objective function of many important learning problems. We establish the convergence rate of a simple Frank-Wolfe variant that uses the open-loop step size strategy $\gamma_t =…

Optimization and Control · Mathematics 2024-04-09 Alejandro Carderera , Mathieu Besançon , Sebastian Pokutta

Decentralized optimization algorithms have received much attention due to the recent advances in network information processing. However, conventional decentralized algorithms based on projected gradient descent are incapable of handling…

Optimization and Control · Mathematics 2018-08-29 Hoi-To Wai , Jean Lafond , Anna Scaglione , Eric Moulines

Some variant of the Frank-Wolfe method for convex optimization problems with adaptive selection of the step parameter corresponding to information about the smoothness of the objective function (the Lipschitz constant of the gradient).…

Optimization and Control · Mathematics 2023-08-01 G. V. Aivazian , F. S. Stonyakin , D. A. Pasechnyuk , M. S. Alkousa , A. M. Raigorodskii

The purpose of this survey is to serve both as a gentle introduction and a coherent overview of state-of-the-art Frank--Wolfe algorithms, also called conditional gradient algorithms, for function minimization. These algorithms are…

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

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

In this paper we provide an introduction to the Frank-Wolfe algorithm, a method for smooth convex optimization in the presence of (relatively) complicated constraints. We will present the algorithm, introduce key concepts, and establish…

Optimization and Control · Mathematics 2023-11-30 Sebastian Pokutta

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

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

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

Learning a deep neural network requires solving a challenging optimization problem: it is a high-dimensional, non-convex and non-smooth minimization problem with a large number of terms. The current practice in neural network optimization…

Machine Learning · Computer Science 2021-02-23 Leonard Berrada , Andrew Zisserman , M. Pawan Kumar

We develop a novel variant of the classical Frank-Wolfe algorithm, which we call spectral Frank-Wolfe, for convex optimization over a spectrahedron. The spectral Frank-Wolfe algorithm has a novel ingredient: it computes a few eigenvectors…

Optimization and Control · Mathematics 2020-08-18 Lijun Ding , Yingjie Fei , Qiantong Xu , Chengrun Yang

Projection-free optimization via different variants of the Frank-Wolfe (FW) method has become one of the cornerstones in large scale optimization for machine learning and computational statistics. Numerous applications within these fields…

Optimization and Control · Mathematics 2021-08-03 Pavel Dvurechensky , Kamil Safin , Shimrit Shtern , Mathias Staudigl