相关论文: Fast block-coordinate Frank-Wolfe algorithm for se…

We consider two greedy algorithms for minimizing a convex function in a bounded convex set: an algorithm by Jones [1992] and the Frank-Wolfe (FW) algorithm. We first consider approximate versions of these algorithms. For smooth convex…

Optimal transport (OT) defines a powerful framework to compare probability distributions in a geometrically faithful way. However, the practical impact of OT is still limited because of its computational burden. We propose a new class of…

Differentiable optimization has received a significant amount of attention due to its foundational role in the domain of machine learning based on neural networks. This paper proposes a differentiable layer, named Differentiable Frank-Wolfe…

Ensuring fairness in matching algorithms is a key challenge in allocating scarce resources and positions. Focusing on Optimal Transport (OT), we introduce a novel notion of group fairness requiring that the probability of matching two…

The complexity in large-scale optimization can lie in both handling the objective function and handling the constraint set. In this respect, stochastic Frank-Wolfe algorithms occupy a unique position as they alleviate both computational…

We develop a novel variant of the classical Frank-Wolfe algorithm, which we call spectral Frank-Wolfe, for convex optimization over a spectrahedron. The spectral Frank-Wolfe algorithm has a novel ingredient: it computes a few eigenvectors…

Optimal transport (OT) has gained popularity due to its various applications in fields such as machine learning, statistics, and signal processing. However, the balanced mass requirement limits its performance in practical problems. To…

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…

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 work studies and develop projection-free algorithms for online learning with linear optimization oracles (a.k.a. Frank-Wolfe) for handling the constraint set. More precisely, this work (i) provides an improved (optimized) variant of an…

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…

Stochastic compositional optimization minimizes objectives of the form $\min_{\bm{x} \in \mathcal{X}} F(\bm{f}(\bm{x}), \bm{x})$, where $\bm{f}$ is accessible only through noisy stochastic queries. Existing methods for this problem assume…

The Frank-Wolfe method is a popular method in sparse constrained optimization, due to its fast per-iteration complexity. However, the tradeoff is that its worst case global convergence is comparatively slow, and importantly, is…

Optimal transport (OT) provides effective tools for comparing and mapping probability measures. We propose to leverage the flexibility of neural networks to learn an approximate optimal transport map. More precisely, we present a new and…

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…

We consider the problem of finding an approximate second-order stationary point of a constrained non-convex optimization problem. We first show that, unlike the gradient descent method for unconstrained optimization, the vanilla projected…

Solving the non-convex optimal power flow (OPF) problem for large-scale power distribution systems is computationally expensive. An alternative is to solve the relaxed convex problem or linear approximated problem, but these methods lead to…

Computing exact Optimal Transport (OT) distances for large-scale datasets is computationally prohibitive. While entropy-regularized alternatives offer speed, they sacrifice precision and frequently suffer from numerical instability in…

We derive a memory-efficient first-order variable splitting algorithm for convex image reconstruction problems with non-smooth regularization terms. The algorithm is based on a primal-dual approach, where one of the dual variables is…

The Frank-Wolfe method has become increasingly useful in statistical and machine learning applications, due to the structure-inducing properties of the iterates, and especially in settings where linear minimization over the feasible set is…