Related papers: Optimization for Robustness Evaluation beyond $\el…

Adversarial training can be used to learn models that are robust against perturbations. For linear models, it can be formulated as a convex optimization problem. Compared to methods proposed in the context of deep learning, leveraging the…

Generalization is a central problem in Machine Learning. Most prediction methods require careful calibration of hyperparameters carried out on a hold-out \textit{validation} dataset to achieve generalization. The main goal of this paper is…

Robust estimation is primarily concerned with providing reliable parameter estimates in the presence of outliers. Numerous robust loss functions have been proposed in regression and classification, along with various computing algorithms.…

Neural networks have been shown to be vulnerable against minor adversarial perturbations of their inputs, especially for high dimensional data under $\ell_\infty$ attacks. To combat this problem, techniques like adversarial training have…

Solving combinatorial optimization (CO) on graphs is among the fundamental tasks for upper-stream applications in data mining, machine learning and operations research. Despite the inherent NP-hard challenge for CO, heuristics,…

Graph neural networks (GNNs) have recently emerged as a promising learning paradigm in learning graph-structured data and have demonstrated wide success across various domains such as recommendation systems, social networks, and electronic…

Adversarial attacks, particularly the Fast Gradient Sign Method (FGSM) and Projected Gradient Descent (PGD) pose significant threats to the robustness of deep learning models in image classification. This paper explores and refines defense…

Due to the highly non-convex nature of large-scale robust parameter estimation, avoiding poor local minima is challenging in real-world applications where input data is contaminated by a large or unknown fraction of outliers. In this paper,…

In deep learning, optimization plays a vital role. By focusing on image classification, this work investigates the pros and cons of the widely used optimizers, and proposes a new optimizer: Perturbated Unit Gradient Descent (PUGD) algorithm…

Physics-informed deep learning often faces optimization challenges due to the complexity of solving partial differential equations (PDEs), which involve exploring large solution spaces, require numerous iterations, and can lead to unstable…

We study the design of computationally efficient algorithms with provable guarantees, that are robust to adversarial (test time) perturbations. While there has been an proliferation of recent work on this topic due to its connections to…

Proximal gradient algorithms (PGA), while foundational for inverse problems like image reconstruction, often yield unstable convergence and suboptimal solutions by violating the critical non-negativity constraint. We identify the gradient…

This study proposes a portfolio optimization framework that integrates advanced deep learning architectures with traditional financial models to enhance risk-adjusted performance. Using historical data from 2015-2023 across equities, ETFs,…

In spite of remarkable progress in deep latent variable generative modeling, training still remains a challenge due to a combination of optimization and generalization issues. In practice, a combination of heuristic algorithms (such as…

Classical assumptions like strong convexity and Lipschitz smoothness often fail to capture the nature of deep learning optimization problems, which are typically non-convex and non-smooth, making traditional analyses less applicable. This…

This manuscript develops a new framework to analyze and design iterative optimization algorithms built on the notion of Integral Quadratic Constraints (IQC) from robust control theory. IQCs provide sufficient conditions for the stability of…

Deep Neural Network (DNN) trained by the gradient descent method is known to be vulnerable to maliciously perturbed adversarial input, aka. adversarial attack. As one of the countermeasures against adversarial attack, increasing the model…

Recent research has used deep learning to develop partial differential equation (PDE) models in science and engineering. The functional form of the PDE is determined by a neural network, and the neural network parameters are calibrated to…

As we seek to deploy machine learning models beyond virtual and controlled domains, it is critical to analyze not only the accuracy or the fact that it works most of the time, but if such a model is truly robust and reliable. This paper…

The field of defense strategies against adversarial attacks has significantly grown over the last years, but progress is hampered as the evaluation of adversarial defenses is often insufficient and thus gives a wrong impression of…