Privacy-Preserving Logistic Regression Training with A Faster Gradient Variant

Logistic regression training over encrypted data has been an attractive idea to security concerns for years. In this paper, we propose a faster gradient variant called $\texttt{quadratic gradient}$ to implement logistic regression training in a homomorphic encryption domain, the core of which can be seen as an extension of the simplified fixed Hessian. We enhance Nesterov's accelerated gradient (NAG) and Adaptive Gradient Algorithm (Adagrad) respectively with this gradient variant and evaluate the enhanced algorithms on several datasets. Experimental results show that the enhanced methods have a state-of-the-art performance in convergence speed compared to the naive first-order gradient methods. We then adopt the enhanced NAG method to implement homomorphic logistic regression training and obtain a comparable result by only $3$ iterations.