相关论文: Heavy Ball Momentum for Conditional Gradient

Online optimization has been a successful framework for solving large-scale problems under computational constraints and partial information. Current methods for online convex optimization require either a projection or exact gradient…

We introduce novel techniques to enhance Frank-Wolfe algorithms by leveraging function smoothness beyond traditional short steps. Our study focuses on Frank-Wolfe algorithms with step sizes that incorporate primal-dual guarantees, offering…

Simple stochastic momentum methods are widely used in machine learning optimization, but their good practical performance is at odds with an absence of theoretical guarantees of acceleration in the literature. In this work, we aim to close…

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 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…

In this paper we consider ill-posed inverse problems, both linear and nonlinear, by a heavy ball method in which a strongly convex regularization function is incorporated to detect the feature of the sought solution. We develop ideas on how…

Data Heterogeneity is a major challenge of Federated Learning performance. Recently, momentum based optimization techniques have beed proved to be effective in mitigating the heterogeneity issue. Along with the model updates, the momentum…

We focus on the optimization problem with smooth, possibly nonconvex objectives and a convex constraint set for which the Euclidean projection operation is practically available. Focusing on this setting, we carry out a general convergence…

This paper focuses on convex constrained optimization problems, where the solution is subject to a convex inequality constraint. In particular, we aim at challenging problems for which both projection into the constrained domain and a…

We present a constructive lower bound of $\Omega(1/\sqrt{\varepsilon})$ for Frank-Wolfe (FW) when both the objective and the constraint set are smooth and strongly convex, showing that the known uniform $\mathcal{O}(1/\sqrt{\varepsilon})$…

Momentum first-order optimization methods are the workhorses in various optimization tasks, e.g., in the training of deep neural networks. Recently, Lucas et al. (2019) proposed a method called Aggregated Heavy-Ball (AggHB) that uses…

In this paper, we revisit the convergence of the Heavy-ball method, and present improved convergence complexity results in the convex setting. We provide the first non-ergodic O(1/k) rate result of the Heavy-ball algorithm with constant…

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 propose an accelerated algorithm with a Frank-Wolfe method as an oracle for solving strongly monotone variational inequality problems. While standard solution approaches, such as projected gradient descent (aka value iteration), involve…

We study the trade-off between convergence rate and sensitivity to stochastic additive gradient noise for first-order optimization methods. Ordinary Gradient Descent (GD) can be made fast-and-sensitive or slow-and-robust by increasing or…

In the present paper, we formulate two versions of Frank--Wolfe algorithm or conditional gradient method to solve the DC optimization problem with an adaptive step size. The DC objective function consists of two components; the first is…

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).…

We investigate algorithmic variants of the Frank-Wolfe (FW) optimization method for pruning convolutional neural networks. This is motivated by the "Lottery Ticket Hypothesis", which suggests the existence of smaller sub-networks within…

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…

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…