# Secure and Efficient Federated Gradient Boosting Decision Trees
## 1 Introduction  
In traditional machine learning, a well-trained machine learning model relies heavily on the data of a large number of users. However, the security and privacy problems of users' data cause many users' data to be sensitive and cannot be directly uploaded to the central server, which greatly limits the flexibility of data application. Therefore, [PERSON] et al. [1] put forward Federated Learning (FL) technology. The goal of FL is to make the model effect as close as possible to that of traditional machine learning methods under the condition of ensuring the safety of users' private data, and to realize collaborative modeling and improve the model effect under the premise of legal compliance. In recent years, FL has been widely used in joint modeling, which can be divided into horizontal federated learning [2], vertical federated learning [3] and federated transfer learning [4].  
However, due to the differences in geographical location and time distribution of clients, the original data of federated learning system is often non-iid, which will adversely affect the accuracy and convergence speed of the model [5], and has been identified as a basic challenge of FL [6]. At present, many federated deep learning algorithms have optimized the problems caused by non-iid data [7; 8; 9].  
Federated learning is influenced by heterogeneous devices and limited network bandwidth, which leads to its computing and communication efficiency becoming the biggest challenge that hinders its practical application. Recently, several federated deep learning algorithms have been studied to reduce the communication efficiency of the model [10; 11; 12].  
At present, most of the research on FL focuses on training deep learning models with privacy protection [13; 14; 15; 16; 17]. Although the deep learning model is very powerful for a series of real-world tasks in the federated scene, it is easily defeated by the \"simpler\" modelwhen faced with tabular datasets, one of which is the gradient boosting decision trees (GBDTs) [18; 19; 20; 21]. The model consists of several decision trees. The decision trees are trained by gradient boosting method, and then weak learners are constructed in turn to minimize the loss function. It has many advantages such as fast training speed, high accuracy and strong interpretability. Many GBDTs frameworks, such as XGBoost [22], LightGBM [23] and CatBoost [24], have been used in different fields [25; 26; 27] and have high learning efficiency and prediction performance.  
Recently, several studies have combined GBDTs with FL, such as GBDTs under secure training in federated setting [28; 29; 30; 31; 32]. These methods usually rely on cryptographic techniques, such as homomorphic encryption (HE) or secure multiparty computing (MPC). This dependence on heavyweight cryptography (such as HE or MPC) often makes methods computationally intensive or require a large number of communication rounds, making it difficult for them to extend to more than a few participants.  
Through the above analysis, the existing federated learning scheme has the problem that the model accuracy is affected by non-iid data. This paper mainly studies the federated learning scheme that can better fit the non-iid data and improve the model accuracy. Secondly, the existing federated optimization methods are mostly based on deep learning algorithms. This paper mainly studies the optimization algorithm of federated GBDTs, which can make up for the shortcomings of slow training speed and unexplained model of federated deep learning algorithms in structured data mining. Finally, the existing GBDTs schemes under secure training in federated environment has the problems of complicated calculation and high communication cost. This paper mainly studies the federated GBDTs scheme which can protect the original data security while reducing the calculation and communication cost.