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.
重新审视全同态加密下的机器学习训练：收敛性保证、差分隐私与高效算法 / Revisiting ML Training under Fully Homomorphic Encryption: Convergence Guarantees, Differential Privacy, and Efficient Algorithms
本文首次从理论上分析了在全同态加密环境下训练机器学习模型的收敛性，并设计了一种结合差分隐私的高效算法，通过使用多项式近似替代非线性函数来适应加密计算，同时避免了昂贵的逐样本梯度裁剪，从而在保护数据隐私的同时实现了可扩展的加密学习。
源自 arXiv: 2605.27782
