Uniform Convergence

Uniform convergence, a core concept in statistical learning theory, aims to establish when the empirical risk (error on training data) accurately reflects the true risk (error on unseen data). Current research focuses on extending uniform convergence beyond traditional settings, investigating its applicability to diverse models like list learners, deep neural networks with various architectures, and online learning algorithms under bandit feedback. This involves developing tighter bounds on sample complexity and exploring alternative approaches when uniform convergence fails, such as leveraging margin-based or risk-functional analyses. These advancements refine our understanding of generalization and improve the design and analysis of machine learning algorithms.