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arXiv · 2610.28878

Actually, All Learnable Distribution Classes Are Privately Learnable

Mohammad Afzali·Hassan Ashtiani·Alex Bie·Gautam Kamath·Peihan Liu·Argyris Mouzakis·Vikrant Singhal
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Abstract

We show that every class of distributions that is learnable up to arbitrarily small target error in total variation distance with finitely many samples is also learnable under ($\varepsilon, δ$)-differential privacy up to arbitrarily small target error with finitely many samples. This proves a conjecture of Ashtiani. Previous work by Bun, Kamath, Mouzakis, and Singhal [arXiv:2402.00267] gave a weak refutation of this conjecture, showing that this implication is not true when learnability is defined with respect to a fixed target error. In contrast, we show that, under the standard definition of learnability, the conjecture is true.

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Mohammad Afzali, Hassan Ashtiani, Alex Bie, Gautam Kamath, Peihan Liu, Argyris Mouzakis, Vikrant Singhal. 2026-10-20. Actually, All Learnable Distribution Classes Are Privately Learnable. https://arxiv.org/abs/2610.28878

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