Norm Penalty

Norm penalties, particularly L1 and L2 penalties, are regularization techniques used in various machine learning models to improve generalization and sparsity. Current research focuses on applying and refining these penalties within diverse contexts, including support vector machines, model averaging, generative adversarial networks, and optimal transport problems, often employing algorithms like stochastic gradient descent and active set methods to efficiently solve the resulting optimization problems. These advancements enhance model robustness, improve training stability, and lead to more accurate and interpretable results across a range of applications, from anomaly detection to high-dimensional data analysis.