Differential Privacy for Pairwise Learning: Non-convex Analysis

Pairwise learning focuses on learning tasks with pairwise loss functions, which depend on pairs of training instances, and naturally fits for modeling relationships between pairs of samples. In this paper, we focus on the privacy of pairwise learning and propose a new differential privacy paradigm for pairwise learning, based on gradient perturbation. We analyze the privacy guarantees from two points of view: the $\ell_2$-sensitivity and the moments accountant method. We further analyze the generalization error, the excess empirical risk, and the excess population risk of our proposed method and give corresponding bounds. By introducing algorithmic stability theory to pairwise differential privacy, our theoretical analysis does not require convex pairwise loss functions, which means that our method is general to both convex and non-convex conditions. Under these circumstances, the utility bounds are better than previous bounds under convexity or strongly convexity assumption, which is an attractive result.