Intrinsic characterization of private PAC sample complexity

Identify a combinatorial measure that characterizes the sample complexity of privately PAC learning every measurable hypothesis class of finite Littlestone dimension, without restricting the class to Cartesian products of VC-one factors, countable evaluation quotients, or candidate-wise small-δ regimes.

Background

The paper investigates whether private PAC sample complexity admits a combinatorial characterization analogous to the VC-dimension characterization of non-private learning. It proves matching bounds up to logarithmic and privacy factors for a restricted class formed from Cartesian products of VC-one components with finite Littlestone dimension and measurable countable quotients.

The paper explicitly leaves the general finite-Littlestone case unresolved, including removal of the structural, measurability, and small-δ restrictions.

References

Identify a combinatorial measure of a class that determines the sample complexity of privately learning it, analogously to the characterization of non-private learning in terms of the VC dimension.

— VALG: An Agentic System for ML Theory Research  (2608.13060 - Zhang et al., 13 Aug 2026) in Section 4, Subsection “Does Differential Privacy Make PAC Learning Much Harder?”, Subproblem 1: The Sample Complexity of Private Learning