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Frank-Wolfe algorithms (FW) are popular first-order methods for solving constrained convex optimization problems that rely on a linear minimization oracle instead of potentially expensive projection-like oracles. Many works have identified…

We derive global convergence bounds for the Frank Wolfe algorithm when training one hidden layer neural networks. When using the ReLU activation function, and under tractable preconditioning assumptions on the sample data set, the linear…

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…

Dictionary learning is a widely used unsupervised learning method in signal processing and machine learning. Most existing works of dictionary learning are in an offline manner. There are mainly two offline ways for dictionary learning. One…

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…

The Frank-Wolfe method (a.k.a. conditional gradient algorithm) for smooth optimization has regained much interest in recent years in the context of large scale optimization and machine learning. A key advantage of the method is that it…

The Frank Wolfe algorithm (FW) is a popular projection-free alternative for solving large-scale constrained optimization problems. However, the FW algorithm suffers from a sublinear convergence rate when minimizing a smooth convex function…

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…

The Frank-Wolfe (FW) algorithm has been widely used in solving nuclear norm constrained problems, since it does not require projections. However, FW often yields high rank intermediate iterates, which can be very expensive in time and space…

In this paper, we consider the general non-oblivious stochastic optimization where the underlying stochasticity may change during the optimization procedure and depends on the point at which the function is evaluated. We develop Stochastic…

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…

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 propose an enhanced zeroth-order stochastic Frank-Wolfe framework to address constrained finite-sum optimization problems, a structure prevalent in large-scale machine-learning applications. Our method introduces a novel double variance…

As a projection-free algorithm, Frank-Wolfe (FW) method, also known as conditional gradient, has recently received considerable attention in the machine learning community. In this dissertation, we study several topics on the FW variants…

We design Local LMO - a new projection-free gradient-type method for constrained optimization. The key algorithmic idea is to replace the global linear minimization oracle over the constraint set used by Frank-Wolfe (FW) with a local linear…

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…

In Bayesian inference, the posterior distributions are difficult to obtain analytically for complex models such as neural networks. Variational inference usually uses a parametric distribution for approximation, from which we can easily…

The Frank-Wolfe algorithm has regained much interest in its use in structurally constrained machine learning applications. However, one major limitation of the Frank-Wolfe algorithm is the slow local convergence property due to the…

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…

We propose an algorithm which appears to be the first bridge between the fields of conditional gradient methods and abs-smooth optimization. Our problem setting is motivated by various applications that lead to nonsmoothness, such as…