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Distance metric learning (DML) is an important task that has found applications in many domains. The high computational cost of DML arises from the large number of variables to be determined and the constraint that a distance metric has to…
Block coordinate descent methods and stochastic subgradient methods have been extensively studied in optimization and machine learning. By combining randomized block sampling with stochastic subgradient methods based on dual averaging, we…
Distributed optimization plays an important role in modern large-scale machine learning and data processing systems by optimizing the utilization of computational resources. One of the classical and popular approaches is Local Stochastic…
This paper considers a distributed stochastic non-convex optimization problem, where the nodes in a network cooperatively minimize a sum of $L$-smooth local cost functions with sparse gradients. By adaptively adjusting the stepsizes…
Stochastic Gradient Descent (SGD) is an out-of-equilibrium algorithm used extensively to train artificial neural networks. However very little is known on to what extent SGD is crucial for to the success of this technology and, in…
Network resource allocation shows revived popularity in the era of data deluge and information explosion. Existing stochastic optimization approaches fall short in attaining a desirable cost-delay tradeoff. Recognizing the central role of…
Adjusting the learning rate schedule in stochastic gradient methods is an important unresolved problem which requires tuning in practice. If certain parameters of the loss function such as smoothness or strong convexity constants are known,…
The distributed nonconvex optimization problem of minimizing a global cost function formed by a sum of $n$ local cost functions by using local information exchange is considered. This problem is an important component of many machine…
Stochastic Gradient Descent (SGD) is one of the many iterative optimization methods that are widely used in solving machine learning problems. These methods display valuable properties and attract researchers and industrial machine learning…
We describe a computationally efficient, stochastic graph-regularization technique that can be utilized for the semi-supervised training of deep neural networks in a parallel or distributed setting. We utilize a technique, first described…
This paper addresses a distributed optimization problem in a communication network where nodes are active sporadically. Each active node applies some learning method to control its action to maximize the global utility function, which is…
Explaining the generalization characteristics of deep learning is an emerging topic in advanced machine learning. There are several unanswered questions about how learning under stochastic optimization really works and why certain…
Stochastic gradient methods (SGMs) are the predominant approaches to train deep learning models. The adaptive versions (e.g., Adam and AMSGrad) have been extensively used in practice, partly because they achieve faster convergence than the…
Previous works on stochastic gradient descent (SGD) often focus on its success. In this work, we construct worst-case optimization problems illustrating that, when not in the regimes that the previous works often assume, SGD can exhibit…
Stochastic gradient descent (SGD) gives an optimal convergence rate when minimizing convex stochastic objectives $f(x)$. However, in terms of making the gradients small, the original SGD does not give an optimal rate, even when $f(x)$ is…
One of the most common methods to train machine learning algorithms today is the stochastic gradient descent (SGD). In a distributed setting, SGD-based algorithms have been shown to converge theoretically under specific circumstances. A…
The mini-batch stochastic gradient descent (SGD) algorithm is widely used in training machine learning models, in particular deep learning models. We study SGD dynamics under linear regression and two-layer linear networks, with an easy…
The increasing size of deep learning models has made distributed training across multiple devices essential. However, current methods such as distributed data-parallel training suffer from large communication and synchronization overheads…
Distributionally robust optimization (DRO) is a powerful technique to train robust models against data distribution shift. This paper aims to solve regularized nonconvex DRO problems, where the uncertainty set is modeled by a so-called…
In this paper, we give a sharp analysis for Stochastic Gradient Descent (SGD) and prove that SGD is able to efficiently escape from saddle points and find an $(\epsilon, O(\epsilon^{0.5}))$-approximate second-order stationary point in…