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Gradient-based methods are well-suited for derivative-free optimization (DFO), where finite-difference (FD) estimates are commonly used as gradient surrogates. Traditional stochastic approximation methods, such as Kiefer-Wolfowitz (KW) and…

Optimization and Control · Mathematics 2025-03-03 Guo Liang , Guangwu Liu , Kun Zhang

We consider the problem of learning a high-dimensional but low-rank matrix from a large-scale dataset distributed over several machines, where low-rankness is enforced by a convex trace norm constraint. We propose DFW-Trace, a distributed…

Distributed, Parallel, and Cluster Computing · Computer Science 2018-05-15 Wenjie Zheng , Aurélien Bellet , Patrick Gallinari

The optimal transport (OT) problem has been used widely for machine learning. It is necessary for computation of an OT problem to solve linear programming with tight mass-conservation constraints. These constraints prevent its application…

Machine Learning · Computer Science 2022-05-30 Takumi Fukunaga , Hiroyuki Kasai

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

The Frank-Wolfe algorithm has regained much interest in its use in structurally constrained machine learning applications. However, one major limitation of the Frank-Wolfe algorithm is the slow local convergence property due to the…

Optimization and Control · Mathematics 2022-10-18 Zhaoyue Chen , Yifan Sun

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

In recent years it was proved that simple modifications of the classical Frank-Wolfe algorithm (aka conditional gradient algorithm) for smooth convex minimization over convex and compact polytopes, converge with linear rate, assuming the…

Optimization and Control · Mathematics 2021-01-08 Dan Garber

This paper focuses on convex constrained optimization problems, where the solution is subject to a convex inequality constraint. In particular, we aim at challenging problems for which both projection into the constrained domain and a…

Optimization and Control · Mathematics 2017-06-13 Tianbao Yang , Qihang Lin , Lijun Zhang

We study the convergence properties of the original and away-step Frank-Wolfe algorithms for linearly constrained stochastic optimization assuming the availability of unbiased objective function gradient estimates. The objective function is…

Optimization and Control · Mathematics 2025-04-08 Natthawut Boonsiriphatthanajaroen , Shane G. Henderson

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 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

This article focuses on a class of distributionally robust optimization (DRO) problems where, unlike the growing body of the literature, the objective function is potentially nonlinear in the distribution. Existing methods to optimize…

Machine Learning · Statistics 2024-11-07 Mohammed Rayyan Sheriff , Peyman Mohajerin Esfahani

Structural support vector machines (SSVMs) are amongst the best performing models for structured computer vision tasks, such as semantic image segmentation or human pose estimation. Training SSVMs, however, is computationally costly,…

Machine Learning · Computer Science 2014-11-19 Neel Shah , Vladimir Kolmogorov , Christoph H. Lampert

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

The forward-backward splitting method (FBS) for minimizing a nonsmooth composite function can be interpreted as a (variable-metric) gradient method over a continuously differentiable function which we call forward-backward envelope (FBE).…

Optimization and Control · Mathematics 2019-11-11 Lorenzo Stella , Andreas Themelis , Panagiotis Patrinos

"Classical" First Order (FO) algorithms of convex optimization, such as Mirror Descent algorithm or Nesterov's optimal algorithm of smooth convex optimization, are well known to have optimal (theoretical) complexity estimates which do not…

Optimization and Control · Mathematics 2013-08-27 Bruce Cox , Anatoli Juditsky , Arkadi Nemirovski

We develop and analyse a first-order algorithm for the A-optimal experimental design problem. The problem is first presented as a special case of a parametric family of optimal design problems for which duality results and optimality…

Computation · Statistics 2013-11-12 Selin Damla Ahipasaoglu

Stochastic Frank-Wolfe is a classical optimization method for solving constrained optimization problems. On the other hand, recent optimizers such as Lion and Muon have gained quite significant popularity in deep learning. In this work,…

Optimization and Control · Mathematics 2026-02-03 Maria-Eleni Sfyraki , Jun-Kun Wang

This paper considers stochastic convex optimization problems where the objective and constraint functions involve expectations with respect to the data indices or environmental variables, in addition to deterministic convex constraints on…

Optimization and Control · Mathematics 2021-07-21 Zeeshan Akhtar , Amrit Singh Bedi , Ketan Rajawat

In this paper, we propose a generalized conditional gradient method for multiobjective optimization, which can be viewed as an improved extension of the classical Frank-Wolfe (conditional gradient) method for single-objective optimization.…

Optimization and Control · Mathematics 2025-03-25 Anteneh Getachew Gebrie , Ellen Hidemi Fukuda