We study privacy amplification for BandMF, i.e., DP-SGD with correlated noise across iterations via a banded correlation matrix. We propose $b$-min-sep subsampling, a new subsampling scheme that generalizes Poisson and balls-in-bins subsampling, extends prior practical batching strategies for BandMF, and enables stronger privacy amplification than cyclic Poisson while preserving the structural properties needed for analysis. We give a near-exact privacy analysis using Monte Carlo accounting, based on a dynamic program that leverages the Markovian structure in the subsampling procedure. We show that $b$-min-sep matches cyclic Poisson subsampling in the high noise regime and achieves strictly better guarantees in the mid-to-low noise regime, with experimental results that bolster our claims. We further show that unlike previous BandMF subsampling schemes, our $b$-min-sep subsampling naturally extends to the multi-attribution user-level privacy setting.

翻译：本研究探讨了BandMF（即通过带状相关矩阵实现迭代间噪声相关的DP-SGD）的隐私增强问题。我们提出了$b$最小间隔子采样方案，该方案推广了泊松采样与球箱采样，扩展了BandMF现有的实用批处理策略，在保持分析所需结构特性的同时，实现了比循环泊松采样更强的隐私增强效果。基于子采样过程中马尔可夫结构的动态规划算法，我们采用蒙特卡洛计算方法给出了近乎精确的隐私分析。研究表明：在高噪声区域$b$最小间隔采样与循环泊松采样效果相当，在中低噪声区域则能获得严格更优的隐私保障，实验结果支撑了该结论。我们进一步证明，与先前BandMF子采样方案不同，$b$最小间隔采样方案可自然扩展到多归因用户级隐私设置场景。