Related papers: A nonsmooth Frank-Wolfe algorithm through a dual c…
We consider smooth convex minimization over compact convex sets, i.e., $\min_{x \in C} f(x)$ with the (vanilla) Frank-Wolfe algorithm. Well-known lower bounds establish a worst-case $\Omega(1/t)$ primal-gap barrier in the general smooth…
We investigate a class of nonconvex optimization problems characterized by a feasible set consisting of level-bounded nonconvex regularizers, with a continuously differentiable objective. We propose a novel hybrid approach to tackle such…
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…
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…
We present a blended conditional gradient approach for minimizing a smooth convex function over a polytope P, combining the Frank--Wolfe algorithm (also called conditional gradient) with gradient-based steps, different from away steps and…
We propose a fast and scalable Polyatomic Frank-Wolfe (P-FW) algorithm for the resolution of high-dimensional LASSO regression problems. The latter improves upon traditional Frank-Wolfe methods by considering generalized greedy steps with…
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…
The conditional gradient algorithm (also known as the Frank-Wolfe algorithm) has recently regained popularity in the machine learning community due to its projection-free property to solve constrained problems. Although many variants of the…
We propose an accelerated algorithm with a Frank-Wolfe method as an oracle for solving strongly monotone variational inequality problems. While standard solution approaches, such as projected gradient descent (aka value iteration), involve…
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…
In this note we observe that for constrained convex minimization problems $\min_{x \in P}f(x)$ over a polytope $P$, dual prices for the linear program $\min_{z \in P} \nabla f(x) z$ obtained from linearization at approximately optimal…
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…
Pruning is a common technique to reduce the compute and storage requirements of Neural Networks. While conventional approaches typically retrain the model to recover pruning-induced performance degradation, state-of-the-art Large Language…
We introduce a new class of Frank-Wolfe algorithms for minimizing differentiable functionals over probability measures. This framework can be shown to encompass a diverse range of tasks in areas such as artificial intelligence,…
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…
We prove that the block-coordinate Frank-Wolfe (BCFW) algorithm converges with state-of-the-art rates in both convex and nonconvex settings under a very mild "block-iterative" assumption. This appears to be the first result on BCFW…
We study constrained stochastic programs where the decision vector at each time slot cannot be chosen freely but is tied to the realization of an underlying random state vector. The goal is to minimize a general objective function subject…
The Frank-Wolfe algorithm is a classic method for constrained optimization problems. It has recently been popular in many machine learning applications because its projection-free property leads to more efficient iterations. In this paper,…
Frank-Wolfe (FW) algorithms have been often proposed over the last few years as efficient solvers for a variety of optimization problems arising in the field of Machine Learning. The ability to work with cheap projection-free iterations and…
This paper is concerned with the Frank--Wolfe algorithm for a special class of {\it non-compact} constrained optimization problems. The notion of asymptotic cone is used to introduce this class of problems as well as to establish that the…