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Stochastic gradient descent (SGD) still is the workhorse for many practical problems. However, it converges slow, and can be difficult to tune. It is possible to precondition SGD to accelerate its convergence remarkably. But many attempts…
The alternating direction method of multipliers (ADMM) is a powerful optimization solver in machine learning. Recently, stochastic ADMM has been integrated with variance reduction methods for stochastic gradient, leading to SAG-ADMM and…
A recent article introduced thecontinuous stochastic gradient method (CSG) for the efficient solution of a class of stochastic optimization problems. While the applicability of known stochastic gradient type methods is typically limited to…
In recent years, there has been considerable interest in designing stochastic first-order algorithms to tackle finite-sum smooth minimax problems. To obtain the gradient estimates, one typically relies on the uniform…
We propose two novel conditional gradient-based methods for solving structured stochastic convex optimization problems with a large number of linear constraints. Instances of this template naturally arise from SDP-relaxations of…
Optimization algorithms are pivotal in advancing various scientific and industrial fields but often encounter obstacles such as trapping in local minima, saddle points, and plateaus (flat regions), which makes the convergence to reasonable…
We propose a new stochastic gradient method for optimizing the sum of a finite set of smooth functions, where the sum is strongly convex. While standard stochastic gradient methods converge at sublinear rates for this problem, the proposed…
Deep neural networks (DNN) are typically optimized using stochastic gradient descent (SGD). However, the estimation of the gradient using stochastic samples tends to be noisy and unreliable, resulting in large gradient variance and bad…
The mirror descent algorithm is known to be effective in situations where it is beneficial to adapt the mirror map to the underlying geometry of the optimization model. However, the effect of mirror maps on the geometry of distributed…
Many machine learning, statistical inference, and portfolio optimization problems require minimization of a composition of expected value functions (CEVF). Of particular interest is the finite-sum versions of such compositional optimization…
Recently, Stochastic Gradient Descent (SGD) and its variants have become the dominant methods in the large-scale optimization of machine learning (ML) problems. A variety of strategies have been proposed for tuning the step sizes, ranging…
In this paper, we establish new convergence results for the quantized distributed gradient descent and suggest a novel strategy of choosing the stepsizes for the high-performance of the algorithm. Under the strongly convexity assumption on…
In recent years, stochastic variance reduction algorithms have attracted considerable attention for minimizing the average of a large but finite number of loss functions. This paper proposes a novel Riemannian extension of the Euclidean…
We investigate the convergence rates and data sample sizes required for training a machine learning model using a stochastic gradient descent (SGD) algorithm, where data points are sampled based on either their loss value or uncertainty…
Stochastic Gradient Descent (SGD) has played a central role in machine learning. However, it requires a carefully hand-picked stepsize for fast convergence, which is notoriously tedious and time-consuming to tune. Over the last several…
We present a convergence rate analysis for biased stochastic gradient descent (SGD), where individual gradient updates are corrupted by computation errors. We develop stochastic quadratic constraints to formulate a small linear matrix…
Two of the most prominent algorithms for solving unconstrained smooth games are the classical stochastic gradient descent-ascent (SGDA) and the recently introduced stochastic consensus optimization (SCO) [Mescheder et al., 2017]. SGDA is…
The Stochastic Gradient Descent method (SGD) and its stochastic variants have become methods of choice for solving finite-sum optimization problems arising from machine learning and data science thanks to their ability to handle large-scale…
The stochastic gradient (SG) method can minimize an objective function composed of a large number of differentiable functions, or solve a stochastic optimization problem, to a moderate accuracy. The block coordinate descent/update (BCD)…
Stochastic gradient descent (SGD) on a low-rank factorization is commonly employed to speed up matrix problems including matrix completion, subspace tracking, and SDP relaxation. In this paper, we exhibit a step size scheme for SGD on a…