Related papers: Frank-Wolfe Method is Automatically Adaptive to Er…
We study a class of convex-concave saddle-point problems of the form $\min_x\max_y \langle Kx,y\rangle+f_{\cal{P}}(x)-h^\ast(y)$ where $K$ is a linear operator, $f_{\cal{P}}$ is the sum of a convex function $f$ with a Lipschitz-continuous…
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…
How can we efficiently mitigate the overhead of gradient communications in distributed optimization? This problem is at the heart of training scalable machine learning models and has been mainly studied in the unconstrained setting. In this…
We introduce a new class of Frank-Wolfe algorithms for minimizing differentiable functionals over probability measures. This framework can be shown to encompass a diverse range of tasks in areas such as artificial intelligence,…
In this paper, we study active set identification results for the away-step Frank-Wolfe algorithm in different settings. We first prove a local identification property that we apply, in combination with a convergence hypothesis, to get an…
We study the conditions under which one is able to efficiently apply variance-reduction and acceleration schemes on finite sum optimization problems. First, we show that, perhaps surprisingly, the finite sum structure by itself, is not…
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…
In this paper, we introduce faster accelerated primal-dual algorithms for minimizing a convex function subject to strongly convex function constraints. Prior to our work, the best complexity bound was $\mathcal{O}(1/{\varepsilon})$,…
In constrained convex optimization, existing methods based on the ellipsoid or cutting plane method do not scale well with the dimension of the ambient space. Alternative approaches such as Projected Gradient Descent only provide a…
Recent studies have shown that proximal gradient (PG) method and accelerated gradient method (APG) with restarting can enjoy a linear convergence under a weaker condition than strong convexity, namely a quadratic growth condition (QGC).…
Performative reinforcement learning is an emerging dynamical decision making framework, which extends reinforcement learning to the common applications where the agent's policy can change the environmental dynamics. Existing works on…
It is known that the curvature of the feasible set in convex optimization allows for algorithms with better convergence rates, and there has been renewed interest in this topic both for offline as well as online problems. In this paper,…
Two of the most fundamental prototypes of greedy optimization are the matching pursuit and Frank-Wolfe algorithms. In this paper, we take a unified view on both classes of methods, leading to the first explicit convergence rates of matching…
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…
In this paper, we develop new affine-invariant algorithms for solving composite convex minimization problems with bounded domain. We present a general framework of Contracting-Point methods, which solve at each iteration an auxiliary…
Mixed-integer nonlinear optimization encompasses a broad class of problems that present both theoretical and computational challenges. We propose a new type of method to solve these problems based on a branch-and-bound algorithm with convex…
Invented some 65 years ago in a seminal paper by Marguerite Straus-Frank and Philip Wolfe, the Frank-Wolfe method recently enjoys a remarkable revival, fuelled by the need of fast and reliable first-order optimization methods in Data…
We introduce a class of first-order methods for smooth constrained optimization that are based on an analogy to non-smooth dynamical systems. Two distinctive features of our approach are that (i) projections or optimizations over the entire…
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…
We consider an optimization problem over measures for emergency response to out-of-hospital cardiac arrest (OHCA), where the goal is to allocate volunteer resources across a spatial region to minimize the probability of death. The problem…