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Stochastic Gradient Descent (SGD) is the workhorse algorithm of deep learning technology. At each step of the training phase, a mini batch of samples is drawn from the training dataset and the weights of the neural network are adjusted…
Compressed Stochastic Gradient Descent (SGD) algorithms have been recently proposed to address the communication bottleneck in distributed and decentralized optimization problems, such as those that arise in federated machine learning.…
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…
We study distributed stochastic gradient descent (SGD) in the master-worker architecture under Byzantine attacks. We consider the heterogeneous data model, where different workers may have different local datasets, and we do not make any…
Stochastic mirror descent (SMD) is a fairly new family of algorithms that has recently found a wide range of applications in optimization, machine learning, and control. It can be considered a generalization of the classical stochastic…
We introduce data structures for solving robust regression through stochastic gradient descent (SGD) by sampling gradients with probability proportional to their norm, i.e., importance sampling. Although SGD is widely used for large scale…
Low-rank matrix estimation is a canonical problem that finds numerous applications in signal processing, machine learning and imaging science. A popular approach in practice is to factorize the matrix into two compact low-rank factors, and…
Stochastic Optimization is a cornerstone of operations research, providing a framework to solve optimization problems under uncertainty. Despite the development of numerous algorithms to tackle these problems, several persistent challenges…
We present a multilevel stochastic gradient descent method for the optimal control of systems governed by partial differential equations under uncertain input data. The gradient descent method used to find the optimal control leverages a…
Stochastic gradient methods have been a popular and powerful choice of optimization methods, aimed at minimizing functions. Their advantage lies in the fact that that one approximates the gradient as opposed to using the full Jacobian…
We consider the stochastic gradient descent (SGD) algorithm driven by a general stochastic sequence, including i.i.d noise and random walk on an arbitrary graph, among others; and analyze it in the asymptotic sense. Specifically, we employ…
Stochastic convex optimization is a basic and well studied primitive in machine learning. It is well known that convex and Lipschitz functions can be minimized efficiently using Stochastic Gradient Descent (SGD). The Normalized Gradient…
We study finite-sum nonconvex optimization problems, where the objective function is an average of $n$ nonconvex functions. We propose a new stochastic gradient descent algorithm based on nested variance reduction. Compared with…
This paper analyzes the trajectories of stochastic gradient descent (SGD) to help understand the algorithm's convergence properties in non-convex problems. We first show that the sequence of iterates generated by SGD remains bounded and…
Mini-batch stochastic gradient descent (SGD) and variants thereof approximate the objective function's gradient with a small number of training examples, aka the batch size. Small batch sizes require little computation for each model update…
A very popular approach for solving stochastic optimization problems is the stochastic gradient descent method (SGD). Although the SGD iteration is computationally cheap and the practical performance of this method may be satisfactory under…
Bayesian computation plays an important role in modern machine learning and statistics to reason about uncertainty. A key computational challenge in Bayesian inference is to develop efficient techniques to approximate, or draw samples from…
Stochastic Gradient Descent (SGD) is one of the most widely used techniques for online optimization in machine learning. In this work, we accelerate SGD by adaptively learning how to sample the most useful training examples at each time…
Modern machine learning often requires training with large batch size, distributed data, and massively parallel compute hardware (like mobile and other edge devices or distributed data centers). Communication becomes a major bottleneck in…
Stochastic bilevel optimization, which captures the inherent nested structure of machine learning problems, is gaining popularity in many recent applications. Existing works on bilevel optimization mostly consider either unconstrained…