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We present a constructive lower bound of $\Omega(1/\sqrt{\varepsilon})$ for Frank-Wolfe (FW) when both the objective and the constraint set are smooth and strongly convex, showing that the known uniform $\mathcal{O}(1/\sqrt{\varepsilon})$…

Optimization and Control · Mathematics 2026-04-14 Jannis Halbey , Daniel Deza , Max Zimmer , Christophe Roux , Bartolomeo Stellato , 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

Aiming at convex optimization under structural constraints, this work introduces and analyzes a variant of the Frank Wolfe (FW) algorithm termed ExtraFW. The distinct feature of ExtraFW is the pair of gradients leveraged per iteration,…

Optimization and Control · Mathematics 2020-12-11 Bingcong Li , Lingda Wang , Georgios B. Giannakis , Zhizhen Zhao

This work studies and develop projection-free algorithms for online learning with linear optimization oracles (a.k.a. Frank-Wolfe) for handling the constraint set. More precisely, this work (i) provides an improved (optimized) variant of an…

Optimization and Control · Mathematics 2026-05-20 Julien Weibel , Pierre Gaillard , Wouter M. Koolen , Adrien Taylor

In this paper, we study the problem of speeding up a type of optimization algorithms called Frank-Wolfe, a conditional gradient method. We develop and employ two novel inner product search data structures, improving the prior fastest…

Data Structures and Algorithms · Computer Science 2022-07-20 Zhao Song , Zhaozhuo Xu , Yuanyuan Yang , Lichen Zhang

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 present and analyze a new generalized Frank-Wolfe method for the composite optimization problem $(P):{\min}_{x\in\mathbb{R}^n}\; f(\mathsf{A} x) + h(x)$, where $f$ is a $\theta$-logarithmically-homogeneous self-concordant barrier,…

Optimization and Control · Mathematics 2021-12-07 Renbo Zhao , Robert M. Freund

Frank-Wolfe algorithms (FW) are popular first-order methods for solving constrained convex optimization problems that rely on a linear minimization oracle instead of potentially expensive projection-like oracles. Many works have identified…

Optimization and Control · Mathematics 2023-09-18 Elias Wirth , Thomas Kerdreux , Sebastian Pokutta

One of the beauties of the projected gradient descent method lies in its rather simple mechanism and yet stable behavior with inexact, stochastic gradients, which has led to its wide-spread use in many machine learning applications.…

Optimization and Control · Mathematics 2019-10-11 Mingrui Zhang , Zebang Shen , Aryan Mokhtari , Hamed Hassani , Amin Karbasi

We introduce a globally-convergent algorithm for optimizing the tree-reweighted (TRW) variational objective over the marginal polytope. The algorithm is based on the conditional gradient method (Frank-Wolfe) and moves pseudomarginals within…

Machine Learning · Statistics 2015-11-26 Rahul G. Krishnan , Simon Lacoste-Julien , David Sontag

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

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

In this paper, we consider non-convex optimization problems under \textit{unknown} yet safety-critical constraints. Such problems naturally arise in a variety of domains including robotics, manufacturing, and medical procedures, where it is…

Machine Learning · Computer Science 2020-06-25 Mohammad Fereydounian , Zebang Shen , Aryan Mokhtari , Amin Karbasi , Hamed Hassani

We propose a variant of the Frank-Wolfe algorithm for solving a class of sparse/low-rank optimization problems. Our formulation includes Elastic Net, regularized SVMs and phase retrieval as special cases. The proposed Primal-Dual Block…

Machine Learning · Computer Science 2019-06-07 Qi Lei , Jiacheng Zhuo , Constantine Caramanis , Inderjit S. Dhillon , Alexandros G. Dimakis

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

Online optimization has been a successful framework for solving large-scale problems under computational constraints and partial information. Current methods for online convex optimization require either a projection or exact gradient…

Machine Learning · Statistics 2018-06-15 Lin Chen , Christopher Harshaw , Hamed Hassani , Amin Karbasi

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

Suppose an agent is in a (possibly unknown) Markov Decision Process in the absence of a reward signal, what might we hope that an agent can efficiently learn to do? This work studies a broad class of objectives that are defined solely as…

Machine Learning · Computer Science 2019-01-29 Elad Hazan , Sham M. Kakade , Karan Singh , Abby Van Soest

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 propose Frank--Wolfe (FW) algorithms with an adaptive Bregman step-size strategy for smooth adaptable (also called: relatively smooth) (weakly-) convex functions. This means that the gradient of the objective function is not necessarily…

Optimization and Control · Mathematics 2026-02-19 Shota Takahashi , Sebastian Pokutta , Akiko Takeda