Related papers: An Inexact Frank-Wolfe Algorithm for Composite Con…
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,…
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,…
We present an exact algorithm for mean-risk optimization subject to a budget constraint, where decision variables may be continuous or integer. The risk is measured by the covariance matrix and weighted by an arbitrary monotone function,…
We consider the problem of minimizing a smooth and convex function over the $n$-dimensional spectrahedron -- the set of real symmetric $n\times n$ positive semidefinite matrices with unit trace, which underlies numerous applications in…
We tackle the Optimal Experiment Design Problem, which consists of choosing experiments to run or observations to select from a finite set to estimate the parameters of a system. The objective is to maximize some measure of information…
We revisit the Frank-Wolfe (FW) optimization under strongly convex constraint sets. We provide a faster convergence rate for FW without line search, showing that a previously overlooked variant of FW is indeed faster than the standard…
Recently, there has been a renewed interest in the machine learning community for variants of a sparse greedy approximation procedure for concave optimization known as {the Frank-Wolfe (FW) method}. In particular, this procedure has been…
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…
We explore computational aspects of maximum likelihood estimation of the mixture proportions of a nonparametric finite mixture model -- a convex optimization problem with old roots in statistics and a key member of the modern data analysis…
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…
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…
Frank-Wolfe methods are projection-free algorithms for constrained optimization whose practical performance often depends critically on the choice of step size. Classical closed-loop step-size rules typically require prior knowledge of a…
It is known that the Frank-Wolfe (FW) algorithm, which is affine-covariant, enjoys accelerated convergence rates when the constraint set is strongly convex. However, these results rely on norm-dependent assumptions, usually incurring…
In this paper, we consider an online optimization process, where the objective functions are not convex (nor concave) but instead belong to a broad class of continuous submodular functions. We first propose a variant of the Frank-Wolfe…
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…
The boosted Frank-Wolfe algorithm accelerates the classical Frank-Wolfe algorithm by better aligning the update direction with the negative gradient. Its analysis, however, has been limited to deterministic convex problems, with step sizes…
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…
We consider optimization problems in which the goal is find a $k$-dimensional subspace of $\mathbb{R}^n$, $k<<n$, which minimizes a convex and smooth loss. Such problems generalize the fundamental task of principal component analysis (PCA)…
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.…
In this paper, we address the problem of minimizing a convex function f over a convex set, with the extra constraint that some variables must be integer. This problem, even when f is a piecewise linear function, is NP-hard. We study an…