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This dissertation studies a fundamental open challenge in deep learning theory: why do deep networks generalize well even while being overparameterized, unregularized and fitting the training data to zero error? In the first part of the…

This essay provides a comprehensive analysis of the optimization and performance evaluation of various routing algorithms within the context of computer networks. Routing algorithms are critical for determining the most efficient path for…

Decentralized optimization is a powerful paradigm that finds applications in engineering and learning design. This work studies decentralized composite optimization problems with non-smooth regularization terms. Most existing gradient-based…

Quasi-convex optimization acts a pivotal part in many fields including economics and finance; the subgradient method is an effective iterative algorithm for solving large-scale quasi-convex optimization problems. In this paper, we…

Deep neural networks (DNNs) enable high performance across domains but remain vulnerable to adversarial perturbations, limiting their use in safety-critical settings. Here, we introduce two quantum-optimization-based models for robust…

Deep learning has achieved remarkable success across a wide range of tasks, but its models often suffer from instability and vulnerability: small changes to the input may drastically affect predictions, while optimization can be hindered by…

Computational imaging has been revolutionized by compressed sensing algorithms, which offer guaranteed uniqueness, convergence, and stability properties. Model-based deep learning methods that combine imaging physics with learned…

Deep neural networks (NN) are extensively used for machine learning tasks such as image classification, perception and control of autonomous systems. Increasingly, these deep NNs are also been deployed in high-assurance applications. Thus,…

We investigate the convergence properties of a class of iterative algorithms designed to minimize a potentially non-smooth and noisy objective function, which may be algebraically intractable and whose values may be obtained as the output…

Deep learning has arguably achieved tremendous success in recent years. In simple words, deep learning uses the composition of many nonlinear functions to model the complex dependency between input features and labels. While neural networks…

Recent advances in Deep Learning have greatly improved performance on various tasks such as object detection, image segmentation, sentiment analysis. The focus of most research directions up until very recently has been on beating…

This book aims to provide an introduction to the topic of deep learning algorithms. We review essential components of deep learning algorithms in full mathematical detail including different artificial neural network (ANN) architectures…

Machine learning can significantly improve performance for decision-making under uncertainty across a wide range of domains. However, ensuring robustness guarantees requires well-calibrated uncertainty estimates, which can be difficult to…

Motivated by applications in machine learning and statistics, we study distributed optimization problems over a network of processors, where the goal is to optimize a global objective composed of a sum of local functions. In these problems,…

This paper considers optimization problems over networks where agents have individual objectives to meet, or individual parameter vectors to estimate, subject to subspace constraints that require the objectives across the network to lie in…

Algorithms have been fundamental to recent global technological advances and, in particular, they have been the cornerstone of technical advances in one field rapidly being applied to another. We argue that algorithms possess fundamentally…

In the last decade, a large body of work has emerged on robustness of neural networks, i.e., checking if the decision remains unchanged when the input is slightly perturbed. However, most of these approaches ignore the confidence of a…

Autonomous vehicles are highly complex systems, required to function reliably in a wide variety of situations. Manually crafting software controllers for these vehicles is difficult, but there has been some success in using deep neural…

Spurred by the enthusiasm surrounding the "Big Data" paradigm, the mathematical and algorithmic tools of online optimization have found widespread use in problems where the trade-off between data exploration and exploitation plays a…

Convolutional and Recurrent, deep neural networks have been successful in machine learning systems for computer vision, reinforcement learning, and other allied fields. However, the robustness of such neural networks is seldom apprised,…