Combinatorial Dimension

Combinatorial dimension focuses on characterizing the learnability of different hypothesis classes by quantifying their complexity using various combinatorial parameters. Current research investigates how these dimensions, such as the Littlestone, VC, and Natarajan dimensions, relate to the sample complexity of learning tasks in various settings, including online learning, list learning, and differentially private learning. This work aims to provide tight bounds on the number of mistakes or samples needed for successful learning, leading to a deeper understanding of the fundamental limits of machine learning algorithms. These findings have significant implications for algorithm design and theoretical analysis across diverse machine learning subfields.