首次证明加密训练的收敛性，兼顾隐私与效率。
Revisiting ML Training under Fully Homomorphic Encryption: Convergence Guarantees, Differential Privacy, and Efficient Algorithms
- 用多项式近似激活和损失函数，实现加密环境下的梯度下降。
- 无需逐样本裁剪梯度，仍保持差分隐私且计算更高效。
- 提供无需数据依赖的超参选择，适合敏感数据场景使用。
我们首次对全同态加密（FHE）下的机器学习训练进行了理论收敛分析，并提出一种针对加密计算设计的差分隐私（DP）训练算法。该方法在保持与标准差分隐私梯度下降（DP-GD）相当性能的同时，提升了计算效率。特别地，我们证明了采用激活函数和损失函数多项式近似后的近似梯度下降的收敛性，这是FHE兼容所必需的。为保障下游任务的隐私性，我们整合差分隐私机制，避免了代价高昂的逐样本梯度裁剪，从而支持可扩展的加密学习。此外，我们还提供了不依赖数据的超参数选择策略以及理论上合理的多项式逼近方法，这些成果可能具有独立研究价值。上述贡献共同推进了高效、私密且安全的敏感数据机器学习的可行性。
原文摘要 · Abstract (English)
We present the first theoretical convergence analysis of machine learning training under fully homomorphic encryption (FHE), combined with a differentially private (DP) training algorithm tailored to encrypted computation. Our approach improves computational efficiency over standard differentially private gradient descent (DP-GD) while achieving comparable utility. In particular, we prove convergence of approximate gradient descent using polynomial approximations of activation and loss functions, which are required for FHE compatibility. To preserve privacy in downstream tasks, we integrate differential privacy without relying on costly per-sample gradient clipping, enabling scalable encrypted learning. We also provide data-independent hyperparameter selection and theoretically grounded strategies for polynomial approximation which can be of independent interest. Together, these contributions advance the feasibility of efficient, private, and secure machine learning on sensitive data.
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