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Decentralized optimization algorithms have received much attention due to the recent advances in network information processing. However, conventional decentralized algorithms based on projected gradient descent are incapable of handling…
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…
We propose a novel and efficient training method for RNNs by iteratively seeking a local minima on the loss surface within a small region, and leverage this directional vector for the update, in an outer-loop. We propose to utilize the…
Frank-Wolfe algorithm (FW) and its variants have gained a surge of interests in machine learning community due to its projection-free property. Recently people have reduced the gradient evaluation complexity of FW algorithm to…
This paper studies the empirical efficacy and benefits of using projection-free first-order methods in the form of Conditional Gradients, a.k.a. Frank-Wolfe methods, for training Neural Networks with constrained parameters. We draw…
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.…
As a projection-free algorithm, Frank-Wolfe (FW) method, also known as conditional gradient, has recently received considerable attention in the machine learning community. In this dissertation, we study several topics on the FW variants…
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 provide a sub-gradient based algorithm to solve general constrained convex optimization without taking projections onto the domain set. The well studied Frank-Wolfe type algorithms also avoid projections. However, they are…
This paper considers distributed stochastic optimization, in which a number of agents cooperate to optimize a global objective function through local computations and information exchanges with neighbors over a network. Stochastic…
One of the beauties of the projected gradient descent method lies in its rather simple mechanism and yet stable behavior with inexact, stochastic gradients, which has led to its wide-spread use in many machine learning applications.…
The Frank-Wolfe (FW) method is a popular approach for solving optimization problems with structured constraints that arise in machine learning applications. In recent years, stochastic versions of FW have gained popularity, motivated by…
This paper proposes a distributed stochastic projection-free algorithm for large-scale constrained finite-sum optimization whose constraint set is complicated such that the projection onto the constraint set can be expensive. The global…
Recently, there has been a renewed interest in the machine learning community for variants of a sparse greedy approximation procedure for concave optimization known as {the Frank-Wolfe (FW) method}. In particular, this procedure has been…
The Frank-Wolfe algorithm has become a popular first-order optimization algorithm for it is simple and projection-free, and it has been successfully applied to a variety of real-world problems. Its main drawback however lies in its…
We introduce a new projection-free (Frank-Wolfe) method for optimizing structured nonconvex functions that are expressed as a difference of two convex functions. This problem class subsumes smooth nonconvex minimization, positioning our…
The Frank-Wolfe optimization algorithm has recently regained popularity for machine learning applications due to its projection-free property and its ability to handle structured constraints. However, in the stochastic learning setting, it…
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…
The Frank-Wolfe method and its extensions are well-suited for delivering solutions with desirable structural properties, such as sparsity or low-rank structure. We introduce a new variant of the Frank-Wolfe method that combines Frank-Wolfe…
The stochastic Frank-Wolfe method has recently attracted much general interest in the context of optimization for statistical and machine learning due to its ability to work with a more general feasible region. However, there has been a…