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We study distributed optimization algorithms for minimizing the average of \emph{heterogeneous} functions distributed across several machines with a focus on communication efficiency. In such settings, naively using the classical stochastic…

Recent developments on large-scale distributed machine learning applications, e.g., deep neural networks, benefit enormously from the advances in distributed non-convex optimization techniques, e.g., distributed Stochastic Gradient Descent…

Stochastic Gradient Descent (SGD) is arguably the most popular of the machine learning methods applied to training deep neural networks (DNN) today. It has recently been demonstrated that SGD can be statistically biased so that certain…

Gradient Descent (GD) and Conjugate Gradient (CG) methods are among the most effective iterative algorithms for solving unconstrained optimization problems, particularly in machine learning and statistical modeling, where they are employed…

This paper presents a methodology for selecting the mini-batch size that minimizes Stochastic Gradient Descent (SGD) learning time for single and multiple learner problems. By decoupling algorithmic analysis issues from hardware and…

We study a distributed consensus-based stochastic gradient descent (SGD) algorithm and show that the rate of convergence involves the spectral properties of two matrices: the standard spectral gap of a weight matrix from the network…

With an increasing demand for training powers for deep learning algorithms and the rapid growth of computation resources in data centers, it is desirable to dynamically schedule different distributed deep learning tasks to maximize resource…

The training of modern deep learning neural network calls for large amounts of computation, which is often provided by GPUs or other specific accelerators. To scale out to achieve faster training speed, two update algorithms are mainly…

Stochastic Gradient Descent (SGD) is a workhorse in machine learning, yet its slow convergence can be a computational bottleneck. Variance reduction techniques such as SAG, SVRG and SAGA have been proposed to overcome this weakness,…

Deep Metric Learning (DML) methods have been proven relevant for visual similarity learning. However, they sometimes lack generalization properties because they are trained often using an inappropriate sample selection strategy or due to…

Stochastic gradient descent (SGD) method is popular for solving non-convex optimization problems in machine learning. This work investigates SGD from a viewpoint of graduated optimization, which is a widely applied approach for non-convex…

Stochastic gradient descent (SGD) with stochastic momentum is popular in nonconvex stochastic optimization and particularly for the training of deep neural networks. In standard SGD, parameters are updated by improving along the path of the…

We present a theoretical analysis of some popular adaptive Stochastic Gradient Descent (SGD) methods in the small learning rate regime. Using the stochastic modified equations framework introduced by Li et al., we derive effective…

Convergence detection of iterative stochastic optimization methods is of great practical interest. This paper considers stochastic gradient descent (SGD) with a constant learning rate and momentum. We show that there exists a transient…

Sufficient dimension reduction (SDR) using distance covariance (DCOV) was recently proposed as an approach to dimension-reduction problems. Compared with other SDR methods, it is model-free without estimating link function and does not…

Stochastic gradient descent (SGD) is one of the most popular algorithms in modern machine learning. The noise encountered in these applications is different from that in many theoretical analyses of stochastic gradient algorithms. In this…

We analyze a batched variant of Stochastic Gradient Descent (SGD) with weighted sampling distribution for smooth and non-smooth objective functions. We show that by distributing the batches computationally, a significant speedup in the…

Modern supervised learning techniques, particularly those using deep nets, involve fitting high dimensional labelled data sets with functions containing very large numbers of parameters. Much of this work is empirical. Interesting phenomena…

Approximating Stochastic Gradient Descent (SGD) as a Stochastic Differential Equation (SDE) has allowed researchers to enjoy the benefits of studying a continuous optimization trajectory while carefully preserving the stochasticity of SGD.…

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…