相关论文: Dual Prices for Frank--Wolfe Algorithms

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…

In this paper we consider a class of optimization problems with a strongly convex objective function and the feasible set given by an intersection of a simple convex set with a set given by a number of linear equality and inequality…

Coordinate-wise minimization is a simple popular method for large-scale optimization. Unfortunately, for general (non-differentiable) convex problems it may not find global minima. We present a class of linear programs that coordinate-wise…

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…

The Frank-Wolfe algorithm, a very first optimization method and also known as the conditional gradient method, was introduced by Frank and Wolfe in 1956. Due to its simple linear subproblems, the Frank-Wolfe algorithm has recently been…

In this paper, we study optimization methods consisting of iteratively minimizing surrogates of an objective function. By proposing several algorithmic variants and simple convergence analyses, we make two main contributions. First, we…

We consider the conic linear program given by a closed convex cone in an Euclidean space and a matrix, where vector on the right-hand-side of the constraint system and the vector defining the objective function are subject to change. Using…

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…

Decentralized learning has been studied intensively in recent years motivated by its wide applications in the context of federated learning. The majority of previous research focuses on the offline setting in which the objective function is…

We prove weak duality between two recent convex relaxation methods for bounding the optimal value of a constrained variational problem in which the objective is an integral functional. The first approach, proposed by Valmorbida et al. (IEEE…

We consider the problem of choosing prices of a set of products so as to maximize profit, taking into account self-elasticity and cross-elasticity, subject to constraints on the prices. We show that this problem can be formulated as…

Finite-dimensional linear programs satisfy strong duality (SD) and have the "dual pricing" (DP) property. The (DP) property ensures that, given a sufficiently small perturbation of the right-hand-side vector, there exists a dual solution…

Dynamic Programming (DP) provides standard algorithms to solve Markov Decision Processes. However, these algorithms generally do not optimize a scalar objective function. In this paper, we draw connections between DP and (constrained)…

We develop new accelerated first-order algorithms in the Frank-Wolfe (FW) family for minimizing smooth convex functions over compact convex sets, with a focus on two prominent constraint classes: (1) polytopes and (2) matrix domains given…

Minimizing a function over an intersection of convex sets is an important task in optimization that is often much more challenging than minimizing it over each individual constraint set. While traditional methods such as Frank-Wolfe (FW) or…

In contrast with many other convex optimization classes, state-of-the-art semidefinite programming solvers are yet unable to efficiently solve large scale instances. This work aims to reduce this scalability gap by proposing a novel…

The Frank-Wolfe algorithm has seen a resurgence in popularity due to its ability to efficiently solve constrained optimization problems in machine learning and high-dimensional statistics. As such, there is much interest in establishing…

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…

The conditional gradient algorithm (also known as the Frank-Wolfe algorithm) has recently regained popularity in the machine learning community due to its projection-free property to solve constrained problems. Although many variants of the…

We consider smooth convex minimization over compact convex sets, i.e., $\min_{x \in C} f(x)$ with the (vanilla) Frank-Wolfe algorithm. Well-known lower bounds establish a worst-case $\Omega(1/t)$ primal-gap barrier in the general smooth…