# Privacy-Preserving Logistic Regression Training with A Faster Gradient Variant

arXiv: https://arxiv.org/abs/2201.10838 · HTML: https://mlsanity.com/paper/2201.10838/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 41 references that are in the map.
- First posted on arXiv 26 Jan 2022.

## Builds on (most cited first, 3 of 3)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [High Performance Logistic Regression for Privacy-Preserving Genome Analysis](https://mlsanity.com/paper/2002.05377/) (2020)
- [Faster Secure Data Mining via Distributed Homomorphic Encryption](https://mlsanity.com/paper/2006.10091/) (2020)

## Built on by (most cited first, 7 of 7)

- [Multinomial Logistic Regression Algorithms via Quadratic Gradient](https://mlsanity.com/paper/2208.06828/) (2022)
- [Simplified Quadratic Gradient: A Unified Framework Bridging Gradient Descent and Newton-Type Methods by Synthesizing Hessians and Gradients](https://mlsanity.com/paper/2209.03282/) (2022)
- [Privacy-Preserving CNN Training with Transfer Learning: Multiclass Logistic Regression](https://mlsanity.com/paper/2304.03807/) (2023)
- [Privacy-Preserving 3-Layer Neural Network Training](https://mlsanity.com/paper/2308.09531/) (2023)
- [Quasi-Quadratic Gradient: A New Direction for Accelerating the BFGS Method in Quasi-Newton Optimization](https://mlsanity.com/paper/2604.23922/) (2026)
- [LFFR: Logistic Function For (single-output) Regression](https://mlsanity.com/paper/2407.09955/) (2024)
- [Generalized Quadratic Gradient: A New Direction in Optimization via the Fusion of Positive-Definite Curvature Matrices and Gradients into A Unified Framework](https://mlsanity.com/paper/2608.01552/) (2026)

## Abstract (arXiv)

Training logistic regression over encrypted data has emerged as a prominent approach to addressing security concerns in recent years. In this paper, we introduce an efficient gradient variant, termed the textitquadratic gradient, which is specifically designed for privacy-preserving logistic regression while remaining equally effective in plaintext optimization. By incorporating this quadratic gradient, we enhance Nesterov's Accelerated Gradient (NAG), Adaptive Gradient (AdaGrad), and Adam algorithms. We evaluate these enhanced algorithms across various datasets, with experimental results demonstrating state-of-the-art convergence rates that significantly outperform traditional first-order gradient methods. Furthermore, we apply the enhanced NAG method to implement homomorphic logistic regression training, achieving comparable performance within only four iterations. The proposed quadratic-gradient approach offers a unified framework that synergizes the advantages of first-order gradient methods and second-order Newton-type methods, suggesting broad applicability to diverse numerical optimization tasks.