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Workshop: Theory and Practice of Differential Privacy

Multiclass versus Binary Differentially Private PAC Learning

Satchit Sivakumar · Mark Bun · Marco Gaboradi

Abstract: We show a generic reduction from multiclass differentially private PAC learning to binary private PAC learning. We apply this transformation to a recently proposed binary private PAC learner to obtain a private multiclass learner with sample complexity that has a polynomial dependence on the multiclass Littlestone dimension and a poly-logarithmic dependence on the number of classes. This yields an exponential improvement in the dependence on both parameters over learners from previous work. Our proof extends the notion of $\Psi$-dimension defined in work of Ben-David et al. \cite{Ben} to the online setting and explores its general properties.

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