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Deep learning networks are typically trained by Stochastic Gradient Descent (SGD) methods that iteratively improve the model parameters by estimating a gradient on a very small fraction of the training data. A major roadblock faced when…
Structured non-convex learning problems, for which critical points have favorable statistical properties, arise frequently in statistical machine learning. Algorithmic convergence and statistical estimation rates are well-understood for…
Stochastic gradient descent (SGD) and its variants have established themselves as the go-to algorithms for large-scale machine learning problems with independent samples due to their generalization performance and intrinsic computational…
In this paper, we study the stochastic gradient descent (SGD) method for the nonconvex nonsmooth optimization, and propose an accelerated SGD method by combining the variance reduction technique with Nesterov's extrapolation technique.…
We provide an improved analysis of normalized SGD showing that adding momentum provably removes the need for large batch sizes on non-convex objectives. Then, we consider the case of objectives with bounded second derivative and show that…
Recent work has established an empirically successful framework for adapting learning rates for stochastic gradient descent (SGD). This effectively removes all needs for tuning, while automatically reducing learning rates over time on…
The stochastic gradient descent (SGD) method is a widely used approach for solving stochastic optimization problems, but its convergence is typically slow. Existing variance reduction techniques, such as SAGA, improve convergence by…
Stochastic gradient algorithms are the main focus of large-scale optimization problems and led to important successes in the recent advancement of the deep learning algorithms. The convergence of SGD depends on the careful choice of…
The presence of outliers can potentially significantly skew the parameters of machine learning models trained via stochastic gradient descent (SGD). In this paper we propose a simple variant of the simple SGD method: in each step, first…
In this paper, we propose a generic and simple strategy for utilizing stochastic gradient information in optimization. The technique essentially contains two consecutive steps in each iteration: 1) computing and normalizing each block…
We consider the minimization of an objective function given access to unbiased estimates of its gradient through stochastic gradient descent (SGD) with constant step-size. While the detailed analysis was only performed for quadratic…
The low-rank stochastic semidefinite optimization has attracted rising attention due to its wide range of applications. The nonconvex reformulation based on the low-rank factorization, significantly improves the computational efficiency but…
The performance of stochastic gradient descent (SGD) depends critically on how learning rates are tuned and decreased over time. We propose a method to automatically adjust multiple learning rates so as to minimize the expected error at any…
Private optimization is a topic of major interest in machine learning, with differentially private stochastic gradient descent (DP-SGD) playing a key role in both theory and practice. Furthermore, DP-SGD is known to be a powerful tool in…
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,…
Stagewise training strategy is widely used for learning neural networks, which runs a stochastic algorithm (e.g., SGD) starting with a relatively large step size (aka learning rate) and geometrically decreasing the step size after a number…
In the vanishing learning rate regime, stochastic gradient descent (SGD) is now relatively well understood. In this work, we propose to study the basic properties of SGD and its variants in the non-vanishing learning rate regime. The focus…
The Barzilai-Borwein (BB) gradient method is efficient for solving large-scale unconstrained problems to the modest accuracy and has a great advantage of being easily extended to solve a wide class of constrained optimization problems. In…
First-order methods such as stochastic gradient descent (SGD) are currently the standard algorithm for training deep neural networks. Second-order methods, despite their better convergence rate, are rarely used in practice due to the…
Self-paced learning and hard example mining re-weight training instances to improve learning accuracy. This paper presents two improved alternatives based on lightweight estimates of sample uncertainty in stochastic gradient descent (SGD):…