Nearly Linear Private Learning of Littlestone Classes

Key points

• Differentially private learning aims to learn from data while protecting individual training examples.1
• Understanding how this dimension controls private sample complexity remains a central question.1
• For classes of Littlestone dimension $d$, the first general upper bound was doubly exponential in $d$ (Bun, Livni, and Moran, FOCS 2020).1
• This yields a private PAC learner for subspaces of dimension at most $d$ over any field, with tight linear dependence on $d$ and no dependence on the ambient dimension, improving the quadratic dependence of Kaplan et al. (STOC 2025).1

Sources (1)

• [1]Nearly Linear Private Learning of Littlestone Classes
  arXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 16, 08:59 AM

  For binary classification, finite Littlestone dimension characterizes approximate private PAC learnability (Alon et al., JACM 2022).

  Differentially private learning aims to learn from data while protecting individual training examples.

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