为马尔可夫链蒙特卡洛算法提供差分隐私保障，关键在目标分布本身需满足隐私要求。
Differential privacy guarantees of Markov chain Monte Carlo algorithms
- 基于吉尔萨诺夫定理与扰动技巧，构建非凸、无界域下的隐私分析新方法。
- 证明迭代n步后状态释放具有与n无关的统一隐私保障，且可评估完整轨迹隐私。
- 适用于无调整朗之万算法和随机梯度朗之万动力学，为隐私保护采样提供实操指南。
本文旨在为马尔可夫链蒙特卡洛（MCMC）算法提供差分隐私（DP）保障。首先，在假设马尔可夫链收敛性条件下，建立MCMC输出样本及其相关蒙特卡洛估计量的DP保证，强调目标分布自身必须具备差分隐私性质。其次，针对无调整朗之万算法（U-Langevin）和随机梯度朗之万动力学（SGLD），利用吉尔萨诺夫定理结合扰动技巧，发展一种新分析方法，实现对非凸、无界域情形下的(Rényi) DP保证。主要结果包括：(i) 当第n步状态被释放时，隐私保证与n无关；(ii) 可对整个链轨迹的隐私进行量化。这些成果为隐私保护型MCMC提供了具体实施依据。
原文摘要 · Abstract (English)
This paper aims to provide differential privacy (DP) guarantees for Markov chain Monte Carlo (MCMC) algorithms. In a first part, we establish DP guarantees on samples output by MCMC algorithms as well as Monte Carlo estimators associated with these methods under assumptions on the convergence properties of the underlying Markov chain. In particular, our results highlight the critical condition of ensuring the target distribution is differentially private itself. In a second part, we specialise our analysis to the unadjusted Langevin algorithm and stochastic gradient Langevin dynamics and establish guarantees on their (Rényi) DP. To this end, we develop a novel methodology based on Girsanov's theorem combined with a perturbation trick to obtain bounds for an unbounded domain and in a non-convex setting. We establish: (i) uniform in $n$ privacy guarantees when the state of the chain after $n$ iterations is released, (ii) bounds on the privacy of the entire chain trajectory. These findings provide concrete guidelines for privacy-preserving MCMC.
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