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Stochastic Gradient Descent (SGD) has become one of the most popular optimization methods for training machine learning models on massive datasets. However, SGD suffers from two main drawbacks: (i) The noisy gradient updates have high…
Sketching and stochastic gradient methods are arguably the most common techniques to derive efficient large scale learning algorithms. In this paper, we investigate their application in the context of nonparametric statistical learning.…
Minimizing empirical risk subject to a set of constraints can be a useful strategy for learning restricted classes of functions, such as monotonic functions, submodular functions, classifiers that guarantee a certain class label for some…
It has been experimentally observed that distributed implementations of mini-batch stochastic gradient descent (SGD) algorithms exhibit speedup saturation and decaying generalization ability beyond a particular batch-size. In this work, we…
We consider the setting where a master wants to run a distributed stochastic gradient descent (SGD) algorithm on $n$ workers, each having a subset of the data. Distributed SGD may suffer from the effect of stragglers, i.e., slow or…
Stochastic descent methods (of the gradient and mirror varieties) have become increasingly popular in optimization. In fact, it is now widely recognized that the success of deep learning is not only due to the special deep architecture of…
In this paper, we provide a theoretical study of noise geometry for minibatch stochastic gradient descent (SGD), a phenomenon where noise aligns favorably with the geometry of local landscape. We propose two metrics, derived from analyzing…
In the past decades, many graph drawing techniques have been proposed for generating aesthetically pleasing graph layouts. However, it remains a challenging task since different layout methods tend to highlight different characteristics of…
The increasing scale of data propels the popularity of leveraging parallelism to speed up the optimization. Minibatch stochastic gradient descent (minibatch SGD) and local SGD are two popular methods for parallel optimization. The existing…
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…
We propose graph-dependent implicit regularisation strategies for distributed stochastic subgradient descent (Distributed SGD) for convex problems in multi-agent learning. Under the standard assumptions of convexity, Lipschitz continuity,…
We consider a distributed learning problem in which the computation is carried out on a system consisting of a master node and multiple worker nodes. In such systems, the existence of slow-running machines called stragglers will cause a…
This paper proposes a novel parallel stochastic gradient descent (SGD) method that is obtained by applying parallel sets of SGD iterations (each set operating on one node using the data residing in it) for finding the direction in each…
Stopping criteria for Stochastic Gradient Descent (SGD) methods play important roles from enabling adaptive step size schemes to providing rigor for downstream analyses such as asymptotic inference. Unfortunately, current stopping criteria…
Graph coarsening is a widely used dimensionality reduction technique for approaching large-scale graph machine learning problems. Given a large graph, graph coarsening aims to learn a smaller-tractable graph while preserving the properties…
In this paper, we propose a novel kernel stochastic gradient descent (SGD) algorithm for large-scale supervised learning with general losses. Compared to traditional kernel SGD, our algorithm improves efficiency and scalability through an…
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…
Graph coarsening reduces the size of a graph while preserving certain properties. Most existing methods preserve either spectral or spatial characteristics. Recent research has shown that preserving topological features helps maintain the…
Stochastic gradient descent (SGD) is a foundational algorithm for large-scale statistical learning and stochastic optimization. However, statistical inference based on SGD iterates remains challenging when stochastic gradients have infinite…
This study explores the sample complexity for two-layer neural networks to learn a generalized linear target function under Stochastic Gradient Descent (SGD), focusing on the challenging regime where many flat directions are present at…