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The Frank-Wolfe algorithm is a classic method for constrained optimization problems. It has recently been popular in many machine learning applications because its projection-free property leads to more efficient iterations. In this paper,…
We propose several variants of the Frank-Wolfe algorithm to minimize a sum of functions. The main proposed algorithm is inspired from the dual averaging scheme of Nesterov adapted for Frank Wolfe in a stochastic setting. A distributed…
Frank-Wolfe methods are projection-free algorithms for constrained optimization whose practical performance often depends critically on the choice of step size. Classical closed-loop step-size rules typically require prior knowledge of a…
Stochastic Frank-Wolfe is a classical optimization method for solving constrained optimization problems. On the other hand, recent optimizers such as Lion and Muon have gained quite significant popularity in deep learning. In this work,…
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…
The optimal power flow (OPF) problem is fundamental in power system operations and planning. Large-scale renewable penetration in distribution networks calls for real-time feedback control, and hence the need for fast and distributed…
There is an emerging need for efficient solutions to stochastic AC Optimal Power Flow ({AC-}OPF) to ensure optimal and reliable grid operations in the presence of increasing demand and generation uncertainty. This paper presents a highly…
In this paper, we focus on solving a distributed convex aggregative optimization problem in a network, where each agent has its own cost function which depends not only on its own decision variables but also on the aggregated function of…
Frank-Wolfe algorithms for convex minimization have recently gained considerable attention from the Optimization and Machine Learning communities, as their properties make them a suitable choice in a variety of applications. However, as…
This paper considers stochastic convex optimization problems where the objective and constraint functions involve expectations with respect to the data indices or environmental variables, in addition to deterministic convex constraints on…
In this paper, we consider Frank-Wolfe-based algorithms for composite convex optimization problems with objective involving a logarithmically-homogeneous, self-concordant functions. Recent Frank-Wolfe-based methods for this class of…
Deep neural networks is today one of the most popular choices in classification, regression and function approximation. However, the training of such deep networks is far from trivial as there are often millions of parameters to tune.…
Multi-category support vector machine (MC-SVM) is one of the most popular machine learning algorithms. There are lots of variants of MC-SVM, although different optimization algorithms were developed for different learning machines. In this…
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…
This work presents the first projection-free algorithm to solve stochastic bi-level optimization problems, where the objective function depends on the solution of another stochastic optimization problem. The proposed $\textbf{S}$tochastic…
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…
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…
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…
Large-scale machine learning training suffers from two prior challenges, specifically for nuclear-norm constrained problems with distributed systems: the synchronization slowdown due to the straggling workers, and high communication costs.…
Learning a deep neural network requires solving a challenging optimization problem: it is a high-dimensional, non-convex and non-smooth minimization problem with a large number of terms. The current practice in neural network optimization…