Transfer Learning In Differential Privacy's Hybrid-Model

TL;DR

This paper introduces a transfer learning approach for differential privacy in hybrid models, enabling effective learning when curator and local data distributions differ, with analysis of sample complexity and methods to reduce it.

Contribution

It proposes the Subsample-Test-Reweigh scheme for transfer learning in hybrid-model differential privacy, leveraging a smooth multiplicative-weights approach and analyzing sample complexity bounds.

Findings

Sample complexity depends on chi-squared divergence between distributions.

The scheme can drastically reduce sample complexity in specific instances.

Theoretical and empirical analysis demonstrate effectiveness of the approach.

Abstract

The 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 curators dataset are drawn from a different distribution than the one of the general population (the local-agents). We give a general scheme -- Subsample-Test-Reweigh -- for this transfer learning problem, which reduces any curator-model DP-learner to a hybrid-model learner in this setting using iterative subsampling and reweighing of the n examples held by the curator based on a smooth variation of the Multiplicative-Weights algorithm (introduced by Bun et al, 2020). Our scheme has a sample complexity which relies on the chi-squared 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.