English
Related papers

Related papers: Lions and Muons: Optimization via Stochastic Frank…

200 papers

Distributed stochastic optimization has drawn great attention recently due to its effectiveness in solving large-scale machine learning problems. Though numerous algorithms have been proposed and successfully applied to general practical…

Optimization and Control · Mathematics 2023-12-15 Kun Huang , Xiao Li , Shi Pu

Non-convex optimization plays a key role in a growing number of machine learning applications. This motivates the identification of specialized structure that enables sharper theoretical analysis. One such identified structure is…

Optimization and Control · Mathematics 2023-06-06 Qiang Fu , Dongchu Xu , Ashia Wilson

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

We analyze two novel randomized variants of the Frank-Wolfe (FW) or conditional gradient algorithm. While classical FW algorithms require solving a linear minimization problem over the domain at each iteration, the proposed method only…

Optimization and Control · Mathematics 2018-03-21 Thomas Kerdreux , Fabian Pedregosa , Alexandre d'Aspremont

In this paper, we show that the Away-step Stochastic Frank-Wolfe Algorithm (ASFW) and Pairwise Stochastic Frank-Wolfe algorithm (PSFW) converge linearly in expectation. We also show that if an algorithm convergences linearly in expectation…

Optimization and Control · Mathematics 2017-03-22 Donald Goldfarb , Garud Iyengar , Chaoxu Zhou

Recent developments in deep learning optimization have brought about radically new algorithms based on the Linear Minimization Oracle (LMO) framework, such as $\sf Muon$ and $\sf Scion$. After over a decade of $\sf Adam$'s dominance, these…

Machine Learning · Computer Science 2025-05-20 Artem Riabinin , Egor Shulgin , Kaja Gruntkowska , Peter Richtárik

In this paper, we present the Stochastic Origin Frank-Wolfe (SOFW) method, which is a special case of the block-coordinate Frank-Wolfe algorithm, applied to the problem of finding equilibrium flow distributions. By significantly reducing…

Optimization and Control · Mathematics 2025-10-03 Igor Ignashin , Demyan Yarmoshik , Andrei Raigorodskii

This paper studies a stochastic algorithm for linearly constrained nonconvex optimization, where the objective function is smooth but only unbiased stochastic gradients with bounded variance are available. We propose a momentum-based…

Optimization and Control · Mathematics 2026-04-16 Chenyang Qiu , Mihitha Maithripala , Zongli Lin

The Frank-Wolfe algorithm has become a popular first-order optimization algorithm for it is simple and projection-free, and it has been successfully applied to a variety of real-world problems. Its main drawback however lies in its…

Optimization and Control · Mathematics 2020-06-25 Cyrille W. Combettes , Sebastian Pokutta

We consider continuous-time dynamics for distributed optimization with set constraints in the paper. To handle the computational complexity of projection-based dynamics due to solving a general quadratic optimization subproblem with…

Optimization and Control · Mathematics 2022-06-24 Guanpu Chen , Peng Yi , Yiguang Hong , Jie Chen

In the present paper, we formulate two versions of Frank--Wolfe algorithm or conditional gradient method to solve the DC optimization problem with an adaptive step size. The DC objective function consists of two components; the first is…

Optimization and Control · Mathematics 2026-02-02 R. Díaz Millán , O. P. Ferreira , J. Ugon

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

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

Owing to their low-complexity iterations, Frank-Wolfe (FW) solvers are well suited for various large-scale learning tasks. When block-separable constraints are present, randomized block FW (RB-FW) has been shown to further reduce complexity…

Optimization and Control · Mathematics 2017-11-22 Liang Zhang , Gang Wang , Daniel Romero , Georgios B. Giannakis

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

Motivated by applications arising from large scale optimization and machine learning, we consider stochastic quasi-Newton (SQN) methods for solving unconstrained convex optimization problems. The convergence analysis of the SQN methods,…

Optimization and Control · Mathematics 2019-10-02 Farzad Yousefian , Angelia Nedić , Uday Shanbhag

The move from hand-designed to learned optimizers in machine learning has been quite successful for gradient-based and -free optimizers. When facing a constrained problem, however, maintaining feasibility typically requires a projection…

Machine Learning · Computer Science 2018-07-31 Patrick Schramowski , Christian Bauckhage , Kristian Kersting

Structured constraints in Machine Learning have recently brought the Frank-Wolfe (FW) family of algorithms back in the spotlight. While the classical FW algorithm has poor local convergence properties, the Away-steps and Pairwise FW…

Optimization and Control · Mathematics 2022-09-09 Fabian Pedregosa , Geoffrey Negiar , Armin Askari , Martin Jaggi

Lion optimizer is a popular learning-based optimization algorithm in machine learning, which shows impressive performance in training many deep learning models. Although convergence property of the Lion optimizer has been studied, its…

Machine Learning · Computer Science 2026-04-17 Feihu Huang , Guanyi Zhang , Songcan Chen

We study the linear convergence of variants of the Frank-Wolfe algorithms for some classes of strongly convex problems, using only affine-invariant quantities. As in Guelat & Marcotte (1986), we show the linear convergence of the standard…

Optimization and Control · Mathematics 2014-01-06 Simon Lacoste-Julien , Martin Jaggi