Privacy Amplification via Iteration for Shuffled and Online PNSGD

TL;DR

This paper extends privacy amplification analysis to shuffled and online projected noisy stochastic gradient descent (PNSGD), providing new privacy guarantees and noise reduction schemes for these settings.

Contribution

It proves privacy guarantees for shuffled PNSGD and introduces a noise reduction scheme for online PNSGD to ensure privacy loss convergence.

Findings

Privacy guarantee for shuffled PNSGD established.

A noise decay scheme for online PNSGD proposed.

Convergence of privacy loss demonstrated in both settings.

Abstract

In this paper, we consider the framework of privacy amplification via iteration, which is originally proposed by Feldman et al. and subsequently simplified by Asoodeh et al. in their analysis via the contraction coefficient. This line of work focuses on the study of the privacy guarantees obtained by the projected noisy stochastic gradient descent (PNSGD) algorithm with hidden intermediate updates. A limitation in the existing literature is that only the early stopped PNSGD has been studied, while no result has been proved on the more widely-used PNSGD applied on a shuffled dataset. Moreover, no scheme has been yet proposed regarding how to decrease the injected noise when new data are received in an online fashion. In this work, we first prove a privacy guarantee for shuffled PNSGD, which is investigated asymptotically when the noise is fixed for each sample size $n$ but reduced at a predetermined rate when $n$ increases, in order to achieve the convergence of privacy loss. We then analyze the online setting and provide a faster decaying scheme for the magnitude of the injected noise that also guarantees the convergence of privacy loss.