Boosting and the Expressive Power of Simple Weak Learners via the gamma-VC Dimension

arXiv:2610.10383v1 Announce Type: new Abstract: Boosting converts weak hypotheses with a small edge over random guessing into highly accurate predictors, but the expressive power of the resulting classifier can depend strongly on the structure of the base class. We study this phenomenon through the gamma-VC dimension introduced by Alon et al. (STOC 2021). Our first result shows that this parameter characterizes the sample complexity for weak-to-strong learning up to a constant factor scaling in gamma. We then sharpen the general relationship between the classic VC dimension and the gamma-VC dimension. Finally, we also give improved upper and lower bounds on the gamma-VC dimension for the fundamental concept classes of decision stumps and axis-parallel rectangles in R^d.

Source: arXiv cs.LG | 2026-10-08