相关论文: Frank-Wolfe Algorithm for the Exact Sparse Problem
Recent papers have shown that the Frank-Wolfe algorithm (FW) with open-loop step-sizes exhibits rates of convergence faster than the iconic $\mathcal{O}(t^{-1})$ rate. In particular, when the minimizer of a strongly convex function over a…
We introduce a new projection-free (Frank-Wolfe) method for optimizing structured nonconvex functions that are expressed as a difference of two convex functions. This problem class subsumes smooth nonconvex minimization, positioning our…
Most existing algorithms for dictionary learning assume that all entries of the (high-dimensional) input data are fully observed. However, in several practical applications (such as hyper-spectral imaging or blood glucose monitoring), only…
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…
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…
Learning sparse combinations is a frequent theme in machine learning. In this paper, we study its associated optimization problem in the distributed setting where the elements to be combined are not centrally located but spread over a…
Consider a sparse multivariate polynomial f with integer coefficients. Assume that f is represented as a "modular black box polynomial", e.g. via an algorithm to evaluate f at arbitrary integer points, modulo arbitrary positive integers.…
The problem of $L_p$-norm constrained coding is to convert signal into code that lies inside an $L_p$-ball and most faithfully reconstructs the signal. Previous works under the name of sparse coding considered the cases of $L_0$ and $L_1$…
Given a way to evaluate an unknown polynomial with integer coefficients, we present new algorithms to recover its nonzero coefficients and corresponding exponents. As an application, we adapt this interpolation algorithm to the problem of…
We study Frank-Wolfe (FW) methods for constrained bilevel optimization when the lower-level problem is solved only approximately, yielding biased and inexact hypergradients. We analyze inexact variants of vanilla FW as well as away-step and…
We study an optimization program over nonnegative Borel measures that encourages sparsity in its solution. Efficient solvers for this program are in increasing demand, as it arises when learning from data generated by a…
We propose a novel Stochastic Frank-Wolfe (a.k.a. conditional gradient) algorithm for constrained smooth finite-sum minimization with a generalized linear prediction/structure. This class of problems includes empirical risk minimization…
The Frank-Wolfe optimization algorithm has recently regained popularity for machine learning applications due to its projection-free property and its ability to handle structured constraints. However, in the stochastic learning setting, it…
Optimization-based problems have become of great interest for signal approximation purposes, as they achieved good accuracy results while being extremely flexible and versatile. In this work, we put our focus on the context of periodic…
A good measure of similarity between data points is crucial to many tasks in machine learning. Similarity and metric learning methods learn such measures automatically from data, but they do not scale well respect to the dimensionality of…
We give a simple proof that the Frank-Wolfe algorithm obtains a stationary point at a rate of $O(1/\sqrt{t})$ on non-convex objectives with a Lipschitz continuous gradient. Our analysis is affine invariant and is the first, to the best of…
Variational inference is a popular technique to approximate a possibly intractable Bayesian posterior with a more tractable one. Recently, boosting variational inference has been proposed as a new paradigm to approximate the posterior by a…
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…
We give a new probabilistic algorithm for interpolating a "sparse" polynomial f given by a straight-line program. Our algorithm constructs an approximation f* of f, such that their difference probably has at most half the number of terms of…
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…