Transfer Learning In Differential Privacy's Hybrid-Model

The \emph{hybrid-model} (Avent et al 2017) in Differential Privacy is a an augmentation of the local-model where in addition to $N$ local-agents we are assisted by one special agent who is in fact a curator holding the sensitive details of $n$ additional individuals. Here we study the problem of machine learning in the hybrid-model where the $n$ individuals in the curator's dataset are drawn from a \emph{different} distribution than the one of the general population (the local-agents). We give a general scheme -- Subsample-Test-Reweigh -- for this \emph{transfer learning} problem, which reduces any curator-model learner to a learner in the hybrid-model using iterative subsampling and reweighing of the $n$ examples held by the curator based on a smooth variation (introduced by Bun et al 2020) of the Multiplicative-Weights algorithm. Our scheme has a sample complexity which relies on the $\chi^2$-divergence between the two distributions. We give worst-case analysis bounds on the sample complexity required for our private reduction. Aiming to reduce said sample complexity, we give two specific instances our sample complexity can be drastically reduced (one instance is analyzed mathematically, while the other - empirically) and pose several directions for follow-up work.