Related papers: Accelerating Frank-Wolfe via Averaging Step Direct…

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…

Conditional gradient algorithms (also often called Frank-Wolfe algorithms) are popular due to their simplicity of only requiring a linear optimization oracle and more recently they also gained significant traction for online learning. While…

Frank--Wolfe methods avoid projections, but over curved feasible regions the full-space linear minimization oracle (LMO) can itself become the computational bottleneck. We introduce random-subspace Frank--Wolfe (RSFW), the first…

In many online learning problems the computational bottleneck for gradient-based methods is the projection operation. For this reason, in many problems the most efficient algorithms are based on the Frank-Wolfe method, which replaces…

In this paper, we focus on solving a distributed convex aggregative optimization problem in a network, where each agent has its own cost function which depends not only on its own decision variables but also on the aggregated function of…

We demonstrate how to scalably solve a class of constrained self-concordant minimization problems using linear minimization oracles (LMO) over the constraint set. We prove that the number of LMO calls of our method is nearly the same as…

In this paper, we consider conditional gradient methods. These are methods that use a linear minimization oracle, which, for a given vector $p \in \mathbb{R}^n$, computes the solution of the subproblem $$\arg \min_{x\in X}{\langle p,x…

Phase retrieval(PR) problem is a kind of ill-condition inverse problem which can be found in various of applications. Utilizing the sparse priority, an algorithm called SWF(Sparse Wirtinger Flow) is proposed in this paper to deal with…

In this paper, the online variants of the classical Frank-Wolfe algorithm are considered. We consider minimizing the regret with a stochastic cost. The online algorithms only require simple iterative updates and a non-adaptive step size…

This paper proposes a distributed stochastic projection-free algorithm for large-scale constrained finite-sum optimization whose constraint set is complicated such that the projection onto the constraint set can be expensive. The global…

Recently, the Frank-Wolfe optimization algorithm was suggested as a procedure to obtain adaptive quadrature rules for integrals of functions in a reproducing kernel Hilbert space (RKHS) with a potentially faster rate of convergence than…

Learning a deep neural network requires solving a challenging optimization problem: it is a high-dimensional, non-convex and non-smooth minimization problem with a large number of terms. The current practice in neural network optimization…

Online optimization has been a successful framework for solving large-scale problems under computational constraints and partial information. Current methods for online convex optimization require either a projection or exact gradient…

We study the Frank-Wolfe algorithm for minimizing a differentiable function with Lipschitz continuous gradient over a compact convex set. To extend classical complexity bounds to certain non-convex functions, we focus on the class of…

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…

When minimizing the sum of a convex and a strongly convex function, or when finding the zero of the sum of a monotone operator and a strongly monotone operator, Chambolle and Pock (2010) and Davis and Yin (2015) proposed accelerated…

Multi-category support vector machine (MC-SVM) is one of the most popular machine learning algorithms. There are lots of variants of MC-SVM, although different optimization algorithms were developed for different learning machines. In this…

In this paper, we consider smooth convex optimization problems with simple constraints and inexactness in the oracle information such as value, partial or directional derivatives of the objective function. We introduce a unifying framework,…

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…

Quasi-Newton methods are widely used for solving convex optimization problems due to their ease of implementation, practical efficiency, and strong local convergence guarantees. However, their global convergence is typically established…