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We present a new accelerated stochastic second-order method that is robust to both gradient and Hessian inexactness, which occurs typically in machine learning. We establish theoretical lower bounds and prove that our algorithm achieves…
In this paper, we propose a new way to obtain optimal convergence rates for smooth stochastic (strong) convex optimization tasks. Our approach is based on results for optimization tasks where gradients have nonrandom noise. In contrast to…
This work establishes new convergence guarantees for gradient descent in smooth convex optimization via a computer-assisted analysis technique. Our theory allows nonconstant stepsize policies with frequent long steps potentially violating…
In order to extract the best possible performance from asynchronous stochastic gradient descent one must increase the mini-batch size and scale the learning rate accordingly. In order to achieve further speedup we introduce a technique that…
We study the problem of minimizing a strongly convex, smooth function when we have noisy estimates of its gradient. We propose a novel multistage accelerated algorithm that is universally optimal in the sense that it achieves the optimal…
We consider unconstrained minimization of smooth convex functions. We propose a novel variational perspective using forced Euler-Lagrange equation that allows for studying high-resolution ODEs. Through this, we obtain a faster convergence…
Stochastic gradient descent (SGD) algorithm and its variations have been effectively used to optimize neural network models. However, with the rapid growth of big data and deep learning, SGD is no longer the most suitable choice due to its…
Optimization plays a key role in machine learning. Recently, stochastic second-order methods have attracted much attention due to their low computational cost in each iteration. However, these algorithms might perform poorly especially if…
We study gradient descent (GD) with a constant stepsize for $\ell_2$-regularized logistic regression with linearly separable data. Classical theory suggests small stepsizes to ensure monotonic reduction of the optimization objective,…
The high-resolution differential equation framework has been proven to be tailor-made for Nesterov's accelerated gradient descent method~(\texttt{NAG}) and its proximal correspondence -- the class of faster iterative shrinkage thresholding…
Stochastic gradient descent (SGD) is a simple and popular method to solve stochastic optimization problems which arise in machine learning. For strongly convex problems, its convergence rate was known to be O(\log(T)/T), by running SGD for…
Many problems encountered in science and engineering can be formulated as estimating a low-rank object (e.g., matrices and tensors) from incomplete, and possibly corrupted, linear measurements. Through the lens of matrix and tensor…
In non-private stochastic convex optimization, stochastic gradient methods converge much faster on interpolation problems -- problems where there exists a solution that simultaneously minimizes all of the sample losses -- than on…
We present a generalization of Nesterov's accelerated gradient descent algorithm. Our algorithm (AGNES) provably achieves acceleration for smooth convex and strongly convex minimization tasks with noisy gradient estimates if the noise…
Vector extrapolation methods are widely used in large-scale simulation studies, and numerous extrapolation-based acceleration techniques have been developed to enhance the convergence of linear and nonlinear fixed-point iterative methods.…
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).…
Asynchronous stochastic gradient descent (ASGD) is a popular parallel optimization algorithm in machine learning. Most theoretical analysis on ASGD take a discrete view and prove upper bounds for their convergence rates. However, the…
Stochastic optimization is a cornerstone of modern machine learning. This paper studies the generalization performance of two classical stochastic optimization algorithms: stochastic gradient descent (SGD) and Nesterov's accelerated…
Stochastic gradient descent (SGD) is a promising method for solving large-scale inverse problems, due to its excellent scalability with respect to data size. In this work, we analyze a new data-driven regularized stochastic gradient descent…
Stochastic Gradient Descent (SGD) has been the method of choice for learning large-scale non-convex models. While a general analysis of when SGD works has been elusive, there has been a lot of recent progress in understanding the…