# Local Differential Privacy-Based Federated Learning under Personalized Settings
###### Abstract
A federated learning framework based on local differential privacy should be adapted to these \"personalized\" privacy settings. Many of the existing federated learning methods, based on local differential privacy, do not take into account the personalized problem [16; 17]. Because of the heterogeneity of data between different clients and the inconsistency of clients' privacy requirements, it is difficult to meet the requirements of all participants with a single federated model, so a personalized method needs to be considered, to meet the personalized requirements of clients. In federated learning based on personalized local differential privacy, when a client sets a low privacy budget, a large noise will be introduced, and the accuracy of the federated model may be low if the server still treats all clients equally. Therefore, it is necessary for the server to take certain measures to adjust the weights of the clients' local models. Following the basic framework of LDP-based federated learning, in this paper we propose several aggregation methods to meet the personalized privacy requirements of clients. According to the characteristics of data distribution, federated learning can be divided into three categories, namely horizontal federated learning, vertical federated learning, and federated transfer learning [18]. Among them, horizontal federated learning is the most common one. The main feature of horizontal federated learning, is that training datasets have the same feature space but different sample spaces. We focus on horizontal federated learning in this paper. We consider both independent identically distributed (IID) datasets and non-independent identically distributed (non-IID) datasets. For IID datasets, we choose the Gaussian mechanism to realize locally differentially private model perturbation. Each client adds Gaussian random noise to the original local model. For non-IID datasets, we choose a probability-based \"symbolized\" function [19] to realize locally differentially private model perturbation. The proposed methods are applied on the server side. Specifically, a weighted average method and a probability-based selection method are proposed for model aggregation. The basic idea of the proposed methods, is to assign different weights to different clients, according to the privacy budgets set by clients. The difference between the two methods, is that in the weighted average method, every client's local model is utilized for model aggregation. If the client chooses a high privacy budget, which means that it does not need a high level of privacy protection, the client will not add too much noise to its local model parameters. Correspondingly, a high weight will be assigned to the client's local model. While in the probability-based selection method, the server randomly selects a few local models for model aggregation. If the client chooses a high privacy budget, a high probability will be assigned to the client's local model, and the client's local model is more likely to be selected by the server. We have conducted experiments on several commonly used datasets, and compared the results of the proposed methods with those of the traditional methods (i.e., the server treats all clients equally). The experimental results show that the weighted average method performs better on IID datasets, and the probability-based selection method performs well on both IID datasets and non-IID datasets. Our contributions are summarized as follows:  
1. Different model perturbation methods are proposed for IID and non-IID data. For IID data, the Gaussian mechanism is applied, to achieve local differential privacy preserving. For non-IID data, the symbolized function is used, to perturb the local model of the client. 2. In order to obtain a federated model under the premise of personalized privacy settings, two model aggregation methods are proposed, namely a weighted average method and a probability-based selection method.