Large pretrained language models (LLMs) have shown surprising In-Context Learning (ICL) ability. An important application in deploying large language models is to augment LLMs with a private database for some specific task.The main problem with this promising commercial use is that LLMs have been shown to memorize their training data and their prompt data are vulnerable to membership inference attacks (MIA) and prompt leaking attacks. In order to deal with this problem, we treat LLMs as untrusted in privacy and propose a locally differentially private framework of in-context learning (LDP-ICL) in the settings where labels are sensitive. Considering the mechanisms of in-context learning in Transformers by gradient descent, we provide an analysis of the trade-off between privacy and utility in such LDP-ICL for classification. Moreover, we apply LDP-ICL to the discrete distribution estimation problem. In the end, we perform several experiments to demonstrate our analysis results

In this paper, we provide two views of constrained differential private (DP) mechanisms. The first one is as belief revision. A constrained DP mechanism is obtained by standard probabilistic conditioning, and hence can be naturally implemented by Monte Carlo algorithms. The other is as belief update. A constrained DP is defined according to l2-distance minimization postprocessing or projection and hence can be naturally implemented by optimization algorithms. The main advantage of these two perspectives is that we can make full use of the machinery of belief revision and update to show basic properties for constrained differential privacy especially some important new composition properties. Within the framework established in this paper, constrained DP algorithms in the literature can be classified either as belief revision or belief update. At the end of the paper, we demonstrate their differences especially in utility on a couple of scenarios.