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Stochastic gradient descent with momentum (SGDM) methods have become fundamental optimization tools in machine learning, combining the computational efficiency of stochastic gradients with the acceleration benefits of momentum. Despite…
Stochastic gradient methods (SGMs) have been extensively used for solving stochastic problems or large-scale machine learning problems. Recent works employ various techniques to improve the convergence rate of SGMs for both convex and…
We combine two advanced ideas widely used in optimization for machine learning: shuffling strategy and momentum technique to develop a novel shuffling gradient-based method with momentum, coined Shuffling Momentum Gradient (SMG), for…
Smooth finite-sum optimization has been widely studied in both convex and nonconvex settings. However, existing lower bounds for finite-sum optimization are mostly limited to the setting where each component function is (strongly) convex,…
We propose the stochastic average gradient (SAG) method for optimizing the sum of a finite number of smooth convex functions. Like stochastic gradient (SG) methods, the SAG method's iteration cost is independent of the number of terms in…
Consider the problem of minimizing the expected value of a (possibly nonconvex) cost function parameterized by a random (vector) variable, when the expectation cannot be computed accurately (e.g., because the statistics of the random…
We consider the problem of minimizing a continuous function given quantum access to a stochastic gradient oracle. We provide two new methods for the special case of minimizing a Lipschitz convex function. Each method obtains a dimension…
We describe a novel optimization method for finite sums (such as empirical risk minimization problems) building on the recently introduced SAGA method. Our method achieves an accelerated convergence rate on strongly convex smooth problems.…
Stochastic Proximal Gradient (SPG) methods have been widely used for solving optimization problems with a simple (possibly non-smooth) regularizer in machine learning and statistics. However, to the best of our knowledge no non-asymptotic…
We provide the first importance sampling variants of variance reduced algorithms for empirical risk minimization with non-convex loss functions. In particular, we analyze non-convex versions of SVRG, SAGA and SARAH. Our methods have the…
We study optimization of finite sums of geodesically smooth functions on Riemannian manifolds. Although variance reduction techniques for optimizing finite-sums have witnessed tremendous attention in the recent years, existing work is…
We propose a stochastic conditional gradient method (CGM) for minimizing convex finite-sum objectives formed as a sum of smooth and non-smooth terms. Existing CGM variants for this template either suffer from slow convergence rates, or…
Stochastic gradient methods with momentum are widely used in applications and at the core of optimization subroutines in many popular machine learning libraries. However, their sample complexities have not been obtained for problems beyond…
In many modern machine learning applications, structures of underlying mathematical models often yield nonconvex optimization problems. Due to the intractability of nonconvexity, there is a rising need to develop efficient methods for…
This paper considers nonconvex distributed constrained optimization over networks, modeled as directed (possibly time-varying) graphs. We introduce the first algorithmic framework for the minimization of the sum of a smooth nonconvex…
The convergence rates for convex and non-convex optimization methods depend on the choice of a host of constants, including step sizes, Lyapunov function constants and momentum constants. In this work we propose the use of factorial powers…
We propose a novel stochastic smoothing accelerated gradient (SSAG) method for general constrained nonsmooth convex composite optimization, and analyze the convergence rates. The SSAG method allows various smoothing techniques, and can deal…
This paper considers a class of constrained convex stochastic composite optimization problems whose objective function is given by the summation of a differentiable convex component, together with a nonsmooth but convex component. The…
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…
This paper studies a stochastic algorithm for linearly constrained nonconvex optimization, where the objective function is smooth but only unbiased stochastic gradients with bounded variance are available. We propose a momentum-based…