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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.…
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…
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…
Maximum consensus estimation plays a critically important role in robust fitting problems in computer vision. Currently, the most prevalent algorithms for consensus maximization draw from the class of randomized hypothesize-and-verify…
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 problems under affine constraints appear in various areas of machine learning. We consider the task of minimizing a smooth strongly convex function F(x) under the affine constraint Kx=b, with an oracle providing evaluations of…
In this paper, we study the problem of finding the Euclidean distance to a convex cone generated by a set of discrete points in $\mathbb{R}^n_+$. In particular, we are interested in problems where the discrete points are the set of feasible…
Greedy optimization methods such as Matching Pursuit (MP) and Frank-Wolfe (FW) algorithms regained popularity in recent years due to their simplicity, effectiveness and theoretical guarantees. MP and FW address optimization over the linear…
We consider the applications of the Frank-Wolfe (FW) algorithm for Apprenticeship Learning (AL). In this setting, we are given a Markov Decision Process (MDP) without an explicit reward function. Instead, we observe an expert that acts…
In this project, we reviewed a paper that deals graph-structured convex optimization (GSCO) problem with the approximate Frank-Wolfe (FW) algorithm. We analyzed and implemented the original algorithm and introduced some extensions based on…
Low-rank approximation of a matrix by means of random sampling has been consistently efficient in its empirical studies by many scientists who applied it with various sparse and structured multipliers, but adequate formal support for this…
This paper considers distributed online convex constrained optimization, in which various agents in a multi-agent system cooperate to minimize a global cost function through communicating with neighbors over a time-varying network. When the…
This paper studies the problem of sampling vector and tensor signals, which is the process of choosing sites in vectors and tensors to place sensors for better recovery. A small core tensor and multiple factor matrices can be used to…
In this paper, we propose new sequential randomized algorithms for convex optimization problems in the presence of uncertainty. A rigorous analysis of the theoretical properties of the solutions obtained by these algorithms, for full…
This article deals with multiobjective composite optimization problems that consist of simultaneously minimizing several objective functions, each of which is composed of a combination of smooth and non-smooth functions. To tackle these…
We address the problem of minimizing a convex function over the space of large matrices with low rank. While this optimization problem is hard in general, we propose an efficient greedy algorithm and derive its formal approximation…
Projection-free optimization algorithms, which are mostly based on the classical Frank-Wolfe method, have gained significant interest in the machine learning community in recent years due to their ability to handle convex constraints that…
We study the linear convergence of Frank-Wolfe algorithms over product polytopes. We analyze two condition numbers for the product polytope, namely the \emph{pyramidal width} and the \emph{vertex-facet distance}, based on the condition…
In this paper, we consider the problem of selecting representatives from a data set for arbitrary supervised/unsupervised learning tasks. We identify a subset $S$ of a data set $A$ such that 1) the size of $S$ is much smaller than $A$ and…
We exploit analogies between first-order algorithms for constrained optimization and non-smooth dynamical systems to design a new class of accelerated first-order algorithms for constrained optimization. Unlike Frank-Wolfe or projected…