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Maximizing a DR-submodular function subject to a general convex set is an NP-hard problem arising from many applications in combinatorial optimization and machine learning. While it is highly desirable to design efficient approximation…

Data Structures and Algorithms · Computer Science 2022-03-29 Donglei Du , Zhicheng Liu , Chenchen Wu , Dachuan Xu , Yang Zhou

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

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

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 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 new version of the Frank-Wolfe method, called the (L0, L1)-Frank-Wolfe algorithm, developed for optimization problems with (L0, L1)-smooth objectives. We establish that this algorithm achieves superior theoretical convergence…

Optimization and Control · Mathematics 2026-05-21 A. A. Vyguzov , F. S. Stonyakin

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

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

In constrained convex optimization, existing methods based on the ellipsoid or cutting plane method do not scale well with the dimension of the ambient space. Alternative approaches such as Projected Gradient Descent only provide a…

Optimization and Control · Mathematics 2021-11-11 Zakaria Mhammedi

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

We address the problem of minimizing a convex smooth function $f(x)$ over a compact polyhedral set $D$ given a stochastic zeroth-order constraint feedback model. This problem arises in safety-critical machine learning applications, such as…

Optimization and Control · Mathematics 2019-12-10 Ilnura Usmanova , Andreas Krause , Maryam Kamgarpour

Minimizing a function over an intersection of convex sets is an important task in optimization that is often much more challenging than minimizing it over each individual constraint set. While traditional methods such as Frank-Wolfe (FW) or…

Optimization and Control · Mathematics 2018-04-11 Gauthier Gidel , Fabian Pedregosa , Simon Lacoste-Julien

We consider the problem of minimizing a difference of (smooth) convex functions over a compact convex feasible region $P$, i.e., $\min_{x \in P} f(x) - g(x)$, with smooth $f$ and Lipschitz continuous $g$. This computational study builds…

Optimization and Control · Mathematics 2025-08-05 Sebastian Pokutta

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

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

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

We study the advantages of accelerated gradient methods, specifically based on the Frank-Wolfe method and projected gradient descent, for privacy and heavy-tailed robustness. Our approaches are as follows: For the Frank-Wolfe method, our…

Statistics Theory · Mathematics 2025-06-04 Laurentiu Andrei Marchis , Po-Ling Loh

We study the effects of constrained optimization formulations and Frank-Wolfe algorithms for obtaining interpretable neural network predictions. Reformulating the Rate-Distortion Explanations (RDE) method for relevance attribution as a…

Machine Learning · Computer Science 2022-02-01 Jan Macdonald , Mathieu Besançon , Sebastian Pokutta

Action-constrained reinforcement learning (RL) is a widely-used approach in various real-world applications, such as scheduling in networked systems with resource constraints and control of a robot with kinematic constraints. While the…

Machine Learning · Computer Science 2021-08-03 Jyun-Li Lin , Wei Hung , Shang-Hsuan Yang , Ping-Chun Hsieh , Xi Liu

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