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Computer Science > Machine Learning
Title: Tractable MCMC for Private Learning with Pure and Gaussian Differential Privacy
(Submitted on 23 Oct 2023 (v1), last revised 1 May 2024 (this version, v2))
Abstract: Posterior sampling, i.e., exponential mechanism to sample from the posterior distribution, provides $\varepsilon$-pure differential privacy (DP) guarantees and does not suffer from potentially unbounded privacy breach introduced by $(\varepsilon,\delta)$-approximate DP. In practice, however, one needs to apply approximate sampling methods such as Markov chain Monte Carlo (MCMC), thus re-introducing the unappealing $\delta$-approximation error into the privacy guarantees. To bridge this gap, we propose the Approximate SAample Perturbation (abbr. ASAP) algorithm which perturbs an MCMC sample with noise proportional to its Wasserstein-infinity ($W_\infty$) distance from a reference distribution that satisfies pure DP or pure Gaussian DP (i.e., $\delta=0$). We then leverage a Metropolis-Hastings algorithm to generate the sample and prove that the algorithm converges in $W_\infty$ distance. We show that by combining our new techniques with a localization step, we obtain the first nearly linear-time algorithm that achieves the optimal rates in the DP-ERM problem with strongly convex and smooth losses.
Submission history
From: Yingyu Lin [view email][v1] Mon, 23 Oct 2023 07:54:39 GMT (47kb)
[v2] Wed, 1 May 2024 05:29:26 GMT (348kb,D)
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